ࡱ> q s Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p %` bjbjNN r,,r$ 4dzdzdzdz(@%$hClll"llllԒ udzZlD]0%l\lll\%@@@dh@@@8  PRACTICE FINAL Multiple Choice Identify the choice that best completes the statement or answers the question. Refer to Figure 1. Figure 1 ____ 1. What is another name for line n? a.line JBc.b.d.AC ____ 2. Name the intersection of lines m and n. a.Kc.Bb.d.D ____ 3. What is another name for line m? a.line JGc.DBb.d.line JB ____ 4. Name a line that contains point A. a.c.Kb.md.DB ____ 5. Name a point NOT contained in  or . a.Kc.Hb.Ad.D ____ 6. Which of these is NOT a way to refer to line BD? a.c.b.md.line JD ____ 7. Name three points that are collinear.  a.B, G, Fc.J, G, Fb.C, D, Hd.J, D, G ____ 8. Name three points that are collinear.  a.M, L, Rc.Q, L, Mb.L, P, Td.R, S, K ____ 9. Are points A, C, D, and F coplanar? Explain.  a.Yes; they all lie on plane P.b.No; they are not on the same line.c.Yes; they all lie on the same face of the pyramid.d.No; three lie on the same face of the pyramid and the fourth does not. Refer to Figure 2. Figure 2 ____ 10. How many planes contain points B, C, and A? a.1c.0b.2d.3 ____ 11. Name an intersection of plane GFL and the plane that contains points A and C. a.line LCc.line ACb.Cd.plane CAB Find the measurement of the segment. ____ 12.  mm,  mm  PS = ? a.32.7 mmc.32.5 mmb.5.1 mmd.32.4 mm Use the number line to find the measure.  ____ 13. RK a.2c.7b.5d.10 Find the coordinates of the midpoint of a segment having the given endpoints. ____ 14.  a.c.b.d. Measure the angle. ____ 15.  a.40c.29b.140d.151 In the figure,  bisects .  ____ 16. If  and , find w. a.7c.52b.14.43d.3.5 In the figure,  and  are opposite rays.  and  bisects .  ____ 17. What bisects ? a.Pc.b.d. ____ 18. Which is NOT true about ? a. is acute.b.c.Point M lies in the interior of .d.It is an angle bisector. ____ 19. If  and , what is ? a.153c.27b.33d.12 ____ 20. If  and , what is ? a.137c.4.2b.12d.43 ____ 21. If  and , what is ? a.5.57c.12b.41d.21.71 Use the figure to find the angles.  ____ 22. Name two acute vertical angles. a.c.b.d. ____ 23. Name a linear pair. a.c.b.d. ____ 24. Name an angle supplementary to . a.c.b.d. ____ 25. Name two obtuse vertical angles. a.c.b.d. ____ 26. The measures of two complementary angles are  and . Find the measures of the angles. a.42, 48c.8.75b.4.25d.96, 84 ____ 27. The measures of two complementary angles are  and . Find the measures of the angles. a.117, 63c.63, 27b.19d.10 Name each polygon by its number of sides. ____ 28.  a.hexagonc.pentagonb.triangled.quadrilateral ____ 29.  a.dodecagonc.hexagonb.pentagond.decagon Name each polygon by its number of sides. Then classify it as convex or concave and regular or irregular. ____ 30.  a.pentagon, convex, regularc.hexagon, convex, regularb.hexagon, concave, regulard.hexagon, convex, irregular ____ 31.  a.quadrilateral, convex, regularc.pentagon, convex, irregularb.quadrilateral, concave, irregulard.quadrilateral, convex, irregular ____ 32.  a.quadrilateral, convex, regularc.pentagon, convex, regularb.quadrilateral, concave, irregulard.quadrilateral, convex, irregular Find the length of each side of the polygon for the given perimeter. ____ 33.  units. Find the length of each side.  a.18 units, 18 units, 13 unitsb.18.66 units, 18.66 units, 13.66 unitsc.27 units, 27 units, 22 unitsd.26 units, 26 units, 21 units ____ 34.  units. Find the length of each side.  a.16 units, 18 units, 14 unitsc.10 units, 18 units, 8 unitsb.12 units, 16 units, 8 unitsd.12 units, 14 units, 10 units Find the circumference of the figure. ____ 35.  a.about c.about b.about d.about  Find the area of the figure. ____ 36.  a.7.13 c.71.3 b.5.4 d.10.8  ____ 37.  a.36c.12b.18d.72 Identify the solid. ____ 38.  a.conec.cylinderb.sphered.prism ____ 39. Name the bases of the solid.  a. and c. and b. and d. and  Name the edges of the solid. ____ 40.  a., , , , , , , , , , , and b., , , and c., , , and d., , , and  Name the faces of the solid. ____ 41.  a.DWUY, DXVZ, UVZY, UVXW, and WXZYb.DWUY, DXVZ, UVZY, and UVXWc.UVZY, UVXW, and WXZYd.DWUY and DXVZ Make a conjecture about the next item in the sequence. ____ 42.  a.1024c.4096b.1025d.1022 Determine whether the conjecture is true or false. Give a counterexample for any false conjecture. ____ 43. Given: a concave polygon Conjecture: It can be regular or irregular. a.False; to be concave the angles cannot be congruent.b.Truec.False; all concave polygons are regular.d.False; a concave polygon has an odd number of sides. ____ 44. Given: Point B is in the interior of . Conjecture:  a.False;  may be obtuse.b.Truec.False; just because it is in the interior does not mean it is on the bisecting line.d.False; . ____ 45. Given:  Conjecture:  a.False; c.False; b.Trued.False;  ____ 46. Given: points R, S, and T Conjecture: R, S, and T are coplanar. a.False; the points do not have to be in a straight line.b.Truec.False; the points to not have to form right angles.d.False; one point may not be between the other two. ____ 47. Given: Two angles are supplementary. Conjecture: They are both acute angles. a.False; either both are right or they are adjacent.b.Truec.False; either both are right or one is obtuse.d.False; they must be vertical angles. ____ 48. Given: Conjecture:  a.False; the angles are not vertical.b.Truec.False; the angles are not complementary.d.False; there is no indication of the measures of the angles. ____ 49. Given: segments RT and ST; twice the measure of . Conjecture: S is the midpoint of segment RT. a.Trueb.False; point S may not be on .c.False; lines do not have midpoints.d.False;  could be the segment bisector of . Use the following statements to write a compound statement for the conjunction or disjunction. Then find its truth value. p: An isosceles triangle has two congruent sides.q: A right angle measures 90r: Four points are always coplanar.s: A decagon has 12 sides. ____ 50. p and r a.An isosceles triangle has two congruent sides and four points are always coplanar; false.b.An isosceles triangle has two congruent sides and a decagon has 12 sides; false.c.An isosceles triangle has two congruent sides and four points are always coplanar; true.d.An isosceles triangle has two congruent sides and a decagon has 12 sides; true. ____ 51.  a.Four points are always coplanar, or a right angle measures 90 and a decagon has 12 sides; false.b.Four points are always coplanar, and a right angle measures 90 or a decagon has 12 sides; true.c.Four points are always coplanar, or a right angle measures 90 and a decagon has 12 sides; true.d.Four points are always coplanar, and a right angle measures 90 or a decagon has 12 sides; false. ____ 52.  a.A right angle measures 90 or four points are always coplanar, and a decagon has 12 sides; false.b.A right angle measures 90 and four points are always coplanar, or a decagon has 12 sides; false.c.A right angle measures 90 and four points are always coplanar, or a decagon has 12 sides; true.d.A right angle measures 90 or four points are always coplanar, and a decagon has 12 sides; true. ____ 53. s or q a.A decagon has 12 sides or a right angle measures 90; true.b.A decagon has 12 sides or a right angle measures 90; false.c.A decagon has 12 sides and a right angle measures 90; true.d.A decagon has 12 sides and a right angle measures 90; false. ____ 54.  a.An isosceles triangle has two congruent sides and a decagon has 12 sides; true.b.An isosceles triangle has two congruent sides or a decagon has 12 sides; false.c.An isosceles triangle has two congruent sides or a decagon has 12 sides; true.d.An isosceles triangle has two congruent sides and a decagon has 12 sides; false. ____ 55.  a.Four points are always coplanar and a right angle measures 90; false.b.Four points are always coplanar and a right angle measures 90; true.c.Four points are always coplanar or a right angle measures 90; false.d.Four points are always coplanar or a right angle measures 90; true. Complete the truth table. ____ 56.  a. b. c. d.  Write the inverse of the conditional statement. Determine whether the inverse is true or false. If it is false, find a counterexample. ____ 57. An equilateral triangle has three congruent sides. a.A non-equilateral triangle has three congruent sides. False; an isosceles triangle has two congruent sides.b.A figure that has three non-congruent sides is not an equilateral triangle. Truec.A non-equilateral triangle does not have three congruent sides. Trued.A figure with three congruent sides is an equilateral triangle. True ____ 58. All country names are capitalized words. a.All capitalized words are country names. False; the first word in the sentence is capitalized.b.All non-capitalized words are not country names. Truec.All non-country names are capitalized words. False; most of the words in the sentence are non-capitalized words.d.All non-country names are non-capitalized words. False; the first word in the sentence is capitalized. ____ 59. Independence Day in the United States is July 4. a.July 4 is not Independence Day in the United States. False; it is Independence Day.b.Non-Independence Day in the United States is not July 4. Truec.Non-Independence Day in the United States is July 4. False; July 4 is Independence Day in the United States.d.Non-July 4 is not Independence Day in the United States. True Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, find a counterexample. ____ 60. If you are 16 years old, then you are a teenager. a.If you are not a teenager, then you are not 16 years old. Trueb.If you are not 16 years old, then you are not a teenager. False; you could be 17 years old.c.If you are not a teenager, then you are 16 years old. Trued.If you are a teenager, then you are 16 years old. False; you could be 17 years old. ____ 61. A converse statement is formed by exchanging the hypothesis and conclusion of the conditional. a.A non-converse statement is not formed by exchanging the hypothesis and conclusion of the conditional. Trueb.A statement not formed by exchanging the hypothesis and conclusion of the conditional is a converse statement. False; an inverse statement is not formed by exchanging the hypothesis and conclusion of the conditional.c.A non-converse statement is formed by exchanging the hypothesis and conclusion of the conditional. False; an inverse statement is formed by negating both the hypothesis and conclusion of the conditional.d.A statement not formed by exchanging the hypothesis and conclusion of the conditional is not a converse statement. True ____ 62. Two angles measuring 180 are supplementary. a.Two angles not measuring 180 are supplementary. Trueb.More than two angles measuring 180 are non-supplementary. Truec.Non-supplementary angles are not two angles measuring 180. Trued.Non-supplementary angles are two angles measuring 180. False; supplementary angles must measure 180. In the figure below, points A, B, C, and F lie on plane P. State the postulate that can be used to show each statement is true.  ____ 63. AandBare collinear. a.If two points lie in a plane then theentire line containing those points liesin that plane.b.Through any two points there isexactly one line.c.If two lines intersect then theirintersection is exactly one point.d.A line contains at least two points. ____ 64. LineADcontains pointsAandD. a.If two lines intersect then theirintersection is exactly one point.b.If two points lie in a plane then theentire line containing those points liesin that plane.c.A line contains at least two points.d.Through any two points there is exactlyone line. Refer to the figure below.  ____ 65. Name all planes intersecting plane CDI. a.ABC, CBG, ADI, FGHc.BAD, GFI, CBG, GFAb.CBA, DAF, HGFd.DAB, CBG, FAD ____ 66. Name all segments parallel to . a.c.b.d. ____ 67. Name all planes intersecting plane . a.c.b.d. ____ 68. Name all segments skew to . a.c.b.d. ____ 69. Name all segments skew to . a.c.b.d. ____ 70. Name all planes intersecting plane . a.c.b.d. ____ 71. Name all segments parallel to . a.c.b.d. Identify the sets of lines to which the given line is a transversal. ____ 72. line j  a.lines m and n nando mandob.lines m and p nandoc.lines id.lines m and n n and o m and o m and p n and p o and p ____ 73. line a  a.lines c and b f and d c and f canddbanddb.lines a and b a and c a and d a and fc.lines f and d c and f canddbanddd.lines c and b fandd ____ 74. In the figure, . Find .  a.c.b.d. Determine whether  and  are parallel, perpendicular, or neither. ____ 75.  a.perpendicularb.parallelc.neither Write an equation in slope-intercept form of the line having the given slope and y-intercept. ____ 76.  a.c.b.d. Write an equation in point-slope form of the line having the given slope that contains the given point. ____ 77.  a.c.b.d. ____ 78.  a.c.b.d. ____ 79.  a.c.b.d. Given the following information, determine which lines, if any, are parallel. State the postulate or theorem that justifies your answer. ____ 80.   a.; congruent corresponding anglesb.; congruent corresponding anglesc.; congruent alternate exterior anglesd.; congruent alternate exterior angles Construct a line perpendicular to m through P. Then find the distance from P to m. ____ 81. Line m contains points  and . Point P has coordinates . a. c. b. d.  Find the distance between the pair of parallel lines. ____ 82.  a.c.b.d. Use a protractor to classify the triangle as acute, equiangular, obtuse, or right. ____ 83.  a.rightc.equiangularb.acuted.obtuse Find the measures of the sides of  and classify the triangle by its sides. ____ 84.  a.equilateralc.isoscelesb.obtused.scalene Find each measure. ____ 85.   a.c.b.d. ____ 86.   a.c.b.d. Identify the congruent triangles in the figure. ____ 87.  a.c.b.d. Determine whether  given the coordinates of the vertices. Explain. ____ 88.  a.Yes; Two sides of triangle PQR and angle PQR are the same measure as the corresponding sides and angle of triangle STU.b.Yes; Each side of triangle PQR is the same length as the corresponding side of triangle STU.c.No; One of the triangles is obtuse.d.No; Each side of triangle PQR is not the same length as the corresponding side of triangle STU. ____ 89. Triangles ABC and AFD are vertical congruent equilateral triangles. Find x and y.  a.c.b.d. ____ 90. Triangle RSU is an equilateral triangle.  bisects . Find x and y.  a.c.b.d. ____ 91. Triangle RSU is an equilateral triangle.  bisects . Find x and y.  a.c.b.d. Identify the type of congruence transformation. ____ 92.  a.reflectionc.rotationb.translationd.not a congruence transformation Position and label the triangle on the coordinate plane. ____ 93. right isosceles  with congruent sides  and  a units long a.c.b.d. ____ 94. isosceles  with base  2b units long a.c.b.d. ____ 95. right  with hypotenuse , leg  4a units long, and leg  one-fourth the other leg a.c.b.d. ____ 96. equilateral  with height c units and base  2d units a.c.b.d. ____ 97. isosceles  with  half the length of the base and bisecting the base a.c.b.d. ____ 98.  is an altitude, , and . Find .  a.34c.18b.32d.31 Determine whether the given measures can be the lengths of the sides of a triangle. Write yes or no. Explain. ____ 99. 3, 9, 10 a.Yes; the third side is the longest.b.No; the sum of the lengths of two sides is not greater than the third.c.No; the first side is not long enough.d.Yes; the sum of the lengths of any two sides is greater than the third. ____ 100. 9.2, 14.5, 17.1 a.Yes; the third side is the longest.b.No; the first side is not long enough.c.Yes; the sum of the lengths of any two sides is greater than the third.d.No; the sum of the lengths of two sides is not greater than the third. Short Answer 101. The graph shows the average daily temperature for different cities. Can you be sure that the temperature of City H is  more than City G? Explain.  102. The longitude-latitude coordinates of Worland, Wyoming are  and of Portland, Maine are . If Worland is one endpoint of a segment and Portland is its midpoint, find the latitude and longitude of the other endpoint. 103. A ray of light is reflected when it hits a mirror. The angle at which the light strikes the mirror is the angle of incidence, i. The angle at which the light is reflected is the angle of reflection, r. The angle of incidence and the angle of reflection are congruent. In the diagram below, if , what is the angle of reflection and   104. In a museum, Nick is looking at a famous painting through a mirror at an angle of  Find the angle the painting makes with the mirror. Also find  and   105. Keith has made a square that has 6-inch cord sides. He bends the square into a circular loop. What is the maximum radius of the circular loop? Round to the nearest tenth. 106. Nick framed a square painting that was 30 centimeters long with a decorative strip. He wants to surround a circular picture frame with the same length of strip. What is the maximum radius of the picture frame? Round to the nearest tenth. Angela has made a large pasta stuffed with pumpkin puree. The pasta was in the form of a right triangular prism. The isometric view of the pasta is shown below.  107. What is the surface area in square feet to the nearest tenth? Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, find a counterexample. 108. Vertical angles are two nonadjacent angles formed by two intersecting lines. 109. Two segments having the same measure are congruent. Write a paragraph proof. 110.  and  are adjacent angles. Prove that point Q is in the interior of . 111. Given: Isosceles triangle GHJ;  is a segment between points K and L on line KL; HG = JG. Prove:   112. Given:  all intersect at point P;  and . Prove:   113. Given: Vertical isosceles triangles;  bisects ; . Prove:   Write a two-column proof. 114. Given: Regular hexagon ABCDFG;  each bisect the hexagon and meet at point H. Prove: If  and , then .  115. .   and . If , prove .  116.  are all parallel to each other.  and . Prove .  117. Given: Square GHJK Prove:   118. Given: W is the midpoint of  and ; . Prove:   119. Given: A regular hexagon; M is the midpoint of  and . Prove:   120. In a group of 150 students, 60 students joined the math club, 54 students joined theater, and 27 students joined both. Draw a Venn diagram to represent the data. 121. A travel agency surveyed a group of 215 high school students. The survey results showed that 86 students have been to Mexico, 106 have been to Canada, and 59 have been to both Mexico and Canada. Draw a Venn diagram to represent the data. 122. Determine the converse of the conditional statement, If a triangle is acute, then it has three acute angles. State whether the converse is true or false. If the converse is false, find a counterexample. 123. Write an example of a conditional statement with its converse. Determine whether statement (3) follows from statements (1) and (2) by the Law of Detachment. If it does not, write invalid. 124. (1) If you are a painter, then you are artistic. (2) If you like colors, then you are artistic. (3) If you like colors, then you are a painter. 125. Emma did not go swimming as it was raining. If it does not rain, then you can go swimming. Write a valid conclusion to the hypothesis If it is not raining, . . . 126. Nick marked six noncoplanar and noncollinear points on a sheet of paper. He joined the points to form a group of connected planes. How many lines and planes will he have? 127. The runways at an airport intersect as shown. The measure of  at the intersection is  Find the measure of   128. A carpenter has constructed a chair like the one shown below. Describe the type of lines formed by the front edge of the seat and a back leg.  In 1995, the circulation of a local newspaper was 1970. In 1997, the circulation was 2330. 129. Predict the circulation for 2001. The graph below shows the use of laptop computers in a state, in hundred thousands, from 1990 to 1999.  130. If the use of laptop computers continues to increase at the same rate, what will be the number of laptop computers used in 2006? John and Nick marked the location of their respective offices on a map. John marked the point  and Nick marked the point  131. Write an equation in the slope-intercept form that models the line between the offices of John and Nick. 132. Identify the obtuse triangles if   and   133. Write a two-column proof for the problem. Given: PQRS is a quadrilateral. Prove:   Write a flow proof. 134. Given:  is isosceles with base ; . Prove:   135. Given:  bisects ; . Prove:   136. Write a paragraph proof for the problem. Given:  Prove:   137. Samantha has cut a pastry into four parts. Suppose  and T is the midpoint of PR. Determine whether  Justify your answer.  Write a two-column proof. 138. Given:  is equilateral;  bisects . Prove: T is the midpoint of .  139. Write a two-column proof for the problem. Given:  is equilateral; . Prove:   . Using the given vertices, identify the congruence transformation. 140.  Write a coordinate proof for the statement. 141. If a line is drawn between the midpoints of two sides of an equiangular triangle, then the resulting triangle is also equiangular. 142. A triangle with coordinates , ,  is isosceles. 143. If a segment from the vertex of the right angle bisects the hypotenuse of a right isosceles triangle, then the resulting two triangles are congruent. 144. Triangle ABC has vertices and  List the angles in order from the greatest to the least measure. 145. A tree 44 meters high cast a shadow 60 meters long, as shown below. Write an inequality relating x and y. Then solve the inequality for x in terms of y.  Write an indirect proof. 146. Given:  Prove:  is positive. 147. Given: ;  Prove:   148. Given: ; A is the midpoint of BF and CD. Prove:   149. Given:  with angle measures as shown Prove:   150. Megan and Sara took part in a 500-meter race on sports day at the school. As the race finished, Megan claimed that she was the winner of the race. The teacher said that according to the stopwatch, Megan took 10 minutes to complete the race, whereas Sara completed the race in 9 minutes. So, Megan was not the winner of the race. Explain whether this is an example of indirect reasoning. PRACTICE FINAL Answer Section MULTIPLE CHOICE 1. ANS: B A line is made up of points with an arrowhead at each end. A, D, and C are points on line n. A line is represented by line DC or  but not just DC. FeedbackAAre those points on line n?BCorrect!CAre those points on line n?DIs that how a line is named? PTS: 1 DIF: Average REF: Lesson 1-1 OBJ: 1-1.1 Identify and model points, lines, and planes. NAT: NCTM GM.2 TOP: Identify and model points, lines, and planes. KEY: Points | Lines | Planes 2. ANS: D Two lines intersect in a point. In this case that is point D. FeedbackAWhat is the intersection of two lines?BIs a line the intersection of two lines?CIs that point on both lines?DCorrect! PTS: 1 DIF: Average REF: Lesson 1-1 OBJ: 1-1.1 Identify and model points, lines, and planes. NAT: NCTM GM.2 TOP: Identify and model points, lines, and planes. KEY: Points | Lines | Planes 3. ANS: D A line is made up of points and has no thickness or width. It is drawn with an arrowhead at each end. J, D, and B are points on line m. A line is represented by line JD or  but not just JD. FeedbackAAre those points on line m?BIs that how you name a line?CIs that how you name a line?DCorrect! PTS: 1 DIF: Average REF: Lesson 1-1 OBJ: 1-1.1 Identify and model points, lines, and planes. NAT: NCTM GM.2 TOP: Identify and model points, lines, and planes. KEY: Points | Lines | Planes 4. ANS: A Line m contains points J, D, and B. Line p contains points G and F. Only line  contains point A. FeedbackACorrect!BIs point A on that line?CIs that a line?DWhat points are on that line? PTS: 1 DIF: Basic REF: Lesson 1-1 OBJ: 1-1.1 Identify and model points, lines, and planes. NAT: NCTM GM.2 TOP: Identify and model points, lines, and planes. KEY: Points | Lines | Planes 5. ANS: C The points not contained in  or  are J, B, and H. K is the plane. FeedbackAIs that a point or the plane?BIs that point on one of the lines listed?CCorrect!DIs that point on one of the lines listed? PTS: 1 DIF: Basic REF: Lesson 1-1 OBJ: 1-1.1 Identify and model points, lines, and planes. NAT: NCTM GM.2 TOP: Identify and model points, lines, and planes. KEY: Points | Lines | Planes 6. ANS: C The proper way to refer to a line is any 2 points on the line with an arrow above them or line such-and-such, where such-and-such is any 2 points on the line. Using three letters is not correct. FeedbackADoes line BD contain point J?BDoes that line contain points B and D?CCorrect!DAre points J and D on line BD? PTS: 1 DIF: Basic REF: Lesson 1-1 OBJ: 1-1.1 Identify and model points, lines, and planes. NAT: NCTM GM.2 TOP: Identify and model points, lines, and planes. KEY: Points | Lines | Planes 7. ANS: A Collinear points are points on the same line. FeedbackACorrect!BAre those points on the same line?CWhat does collinear mean?DAre those points on the same line? PTS: 1 DIF: Average REF: Lesson 1-1 OBJ: 1-1.2 Identify collinear points. NAT: NCTM GM.2 TOP: Identify collinear points. KEY: Collinear Points 8. ANS: A Collinear points are points on the same line. FeedbackACorrect!BAre those points on the same line?CAre those points on the same line?DWhat does collinear mean? PTS: 1 DIF: Average REF: Lesson 1-1 OBJ: 1-1.2 Identify collinear points. NAT: NCTM GM.2 TOP: Identify collinear points. KEY: Collinear Points 9. ANS: D Points that lie on the same plane are said to be coplanar. Three points are always coplanar but if the fourth point is not on the same plane with the first three, they are not all coplanar. FeedbackADo all four points lie on the same plane? Which plane?BDo all four points lie on the same plane? Which plane?CWhat does coplanar mean?DCorrect! PTS: 1 DIF: Average REF: Lesson 1-1 OBJ: 1-1.3 Identify coplanar points. NAT: NCTM GM.2 TOP: Identify coplanar points. KEY: Coplanar Points | Intersecting Lines | Lines in Space 10. ANS: A B, C, and A make up the back face of the prism. FeedbackACorrect!BWhere is the second plane?CDo the points determine a face of the prism?DWhere are the second and third planes? PTS: 1 DIF: Average REF: Lesson 1-1 OBJ: 1-1.4 Identify intersecting lines and planes in space. NAT: NCTM ME.1 TOP: Identify intersecting lines and planes in space. KEY: Planes | Planes in Space 11. ANS: A The intersection of two planes is a line. FeedbackACorrect!BCan the intersection of two planes be a point?CIs point A on plane GFL?DCan the intersection of two planes be a plane? PTS: 1 DIF: Average REF: Lesson 1-1 OBJ: 1-1.4 Identify intersecting lines and planes in space. NAT: NCTM ME.1 TOP: Identify intersecting lines and planes in space. KEY: Planes | Planes in Space 12. ANS: C PS has the same length as PR and RS combined. FeedbackADid you add correctly?BPS contains both PR and RS.CCorrect!DTry adding that again. PTS: 1 DIF: Basic REF: Lesson 1-2 OBJ: 1-2.1 Measure segments. NAT: NCTM ME.2 | NCTM ME.2a TOP: Measure segments. KEY: Measurement | Line Segments 13. ANS: D The distance between two points a and b is  or . FeedbackAYou are looking for the measure, not the midpoint.BYou are looking for the measure, not the half measure.CAdd those numbers again.DCorrect! PTS: 1 DIF: Average REF: Lesson 1-3 OBJ: 1-3.1 Find the distance between two points on a number line. NAT: NCTM GM.2 | NCTM GM.2a TOP: Find the distance between two points on a number line. KEY: Distance | Number Lines | Distance Between Two Points 14. ANS: C The formula for the midpoint between two points  is . FeedbackADid you use the Midpoint Formula?BDid you use the Midpoint Formula correctly?CCorrect!DDo you subtract and then divide by two? PTS: 1 DIF: Average REF: Lesson 1-3 OBJ: 1-3.3 Find the midpoint of a segment. NAT: NCTM ME.1 TOP: Find the midpoint of a segment. KEY: Midpoint | Line Segment 15. ANS: B Use a protractor. Align the 0 on either side of the scale with one side of the angle. Place the center point of the protractor on the vertex. Find where the other side of the angle intersects the scale. Read the scale on which you placed your 0. FeedbackARead the other scale.BCorrect!CBe more precise and read the other scale.DBe more precise. PTS: 1 DIF: Basic REF: Lesson 1-4 OBJ: 1-4.1 Measure angles. NAT: NCTM GM.1 | NCTM GM.1a TOP: Measure angles. KEY: Angles | Measure Angles 16. ANS: A Since  bisects ,  and . Solve for w. FeedbackACorrect!BYou are given the measure of FGH, not KGH.CYou are not finding the measure of FGK. You are finding w.DWhy did you divide by 2? PTS: 1 DIF: Average REF: Lesson 1-4 OBJ: 1-4.3 Identify and use congruent angles. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify and use congruent angles. KEY: Angles | Congruent Angles | Congruency 17. ANS: B A ray bisects an angle. K is the endpoint of that ray, not P. The answer is . FeedbackAIs a bisector a point?BCorrect!CIs P the endpoint of that ray?DIs a bisector an angle? PTS: 1 DIF: Basic REF: Lesson 1-4 OBJ: 1-4.4 Identify and use the bisector of an angle. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify and use the bisector of an angle. KEY: Angle Bisectors 18. ANS: A , so it is obtuse. FeedbackACorrect!BIf answer d is true, then this must be true.CBeing in the interior means being between the two end rays of an angle.DIf answer b is true, then this must be true. PTS: 1 DIF: Basic REF: Lesson 1-4 OBJ: 1-4.4 Identify and use the bisector of an angle. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify and use the bisector of an angle. KEY: Angle Bisectors 19. ANS: C  FeedbackAThat is the measure of JKM.BYou forgot to add in x.CCorrect!DOpposite rays add up to 180. PTS: 1 DIF: Average REF: Lesson 1-4 OBJ: 1-4.4 Identify and use the bisector of an angle. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify and use the bisector of an angle. KEY: Angle Bisectors 20. ANS: D  FeedbackAWhich angle are you looking for?BDid you solve for q instead of the angle measure?CWhich two angles added together equal LKN?DCorrect! PTS: 1 DIF: Average REF: Lesson 1-4 OBJ: 1-4.4 Identify and use the bisector of an angle. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify and use the bisector of an angle. KEY: Angle Bisectors 21. ANS: B  FeedbackAHow many degrees in a straight angle?BCorrect!CDid you solve for x instead of the angle measure?DHow many degrees in a straight angle? PTS: 1 DIF: Average REF: Lesson 1-4 OBJ: 1-4.4 Identify and use the bisector of an angle. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify and use the bisector of an angle. KEY: Angle Bisectors 22. ANS: B Vertical angles are two nonadjacent angles formed by two intersecting lines. Acute angles measure less than 90 degrees. FeedbackAYou are looking for vertical angles, not adjacent angles.BCorrect!CYou are looking for vertical angles, not a linear pair.DWhat is the definition of acute? PTS: 1 DIF: Basic REF: Lesson 1-5 OBJ: 1-5.1 Identify and use special pairs of angles. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify and use special pairs of angles. KEY: Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles 23. ANS: C A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays. FeedbackAYou are looking for a linear pair, not vertical angles.BYou are looking for a linear pair, not just adjacent angles.CCorrect!DYou are looking for a linear pair which, by definition, must be adjacent. PTS: 1 DIF: Average REF: Lesson 1-5 OBJ: 1-5.1 Identify and use special pairs of angles. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify and use special pairs of angles. KEY: Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles 24. ANS: A Supplementary angles are two angles whose measures have a sum of 180. FeedbackACorrect!BWhat is the definition of supplementary?CDo the measures have a sum of 180 degrees?DWhat is the definition of supplementary? PTS: 1 DIF: Basic REF: Lesson 1-5 OBJ: 1-5.1 Identify and use special pairs of angles. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify and use special pairs of angles. KEY: Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles 25. ANS: D Vertical angles are two nonadjacent angles formed by two intersecting lines. Obtuse angles measure greater than 90 degrees. FeedbackAYou are looking for vertical angles, not adjacent angles.BWhat is the definition of obtuse?CYou are looking for vertical angles, not a linear pair.DCorrect! PTS: 1 DIF: Basic REF: Lesson 1-5 OBJ: 1-5.1 Identify and use special pairs of angles. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify and use special pairs of angles. KEY: Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles 26. ANS: A Complementary angles are two angles whose measures have a sum of 90. FeedbackACorrect!BIs that the value of q, or the measure of the angles?CWhat is the definition of complementary?DIs the sum of those angles 90? PTS: 1 DIF: Average REF: Lesson 1-5 OBJ: 1-5.1 Identify and use special pairs of angles. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify and use special pairs of angles. KEY: Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles 27. ANS: C Complementary angles are two angles whose measures have a sum of 90. FeedbackAWhat is the definition of complementary?BDid you find the measures of two angles?CCorrect!DDid you find y or the measures of the angles? PTS: 1 DIF: Average REF: Lesson 1-5 OBJ: 1-5.1 Identify and use special pairs of angles. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify and use special pairs of angles. KEY: Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles 28. ANS: B Count the number of sides to determine the name of the polygon. FeedbackAHow many sides does a hexagon have?BCorrect!CHow many sides does a pentagon have?DCount the number of sides. PTS: 1 DIF: Average REF: Lesson 1-6 OBJ: 1-6.1 Identify polygons. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify polygons. KEY: Polygons | Identify Polygons 29. ANS: A Count the number of sides to determine the name of the polygon. FeedbackACorrect!BCount the number of sides.CHow many sides does a hexagon have?DHow many sides does a decagon have? PTS: 1 DIF: Average REF: Lesson 1-6 OBJ: 1-6.1 Identify polygons. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify polygons. KEY: Polygons | Identify Polygons 30. ANS: C Suppose the line containing each side is drawn. If any of the lines contain any point in the interior of the polygon, then it is concave. Otherwise it is convex. A convex polygon in which all the sides are congruent and all the angles are congruent is called a regular polygon. FeedbackACount the number of sides.BIf it is concave, lines drawn from the segments would pass through the polygon.CCorrect!DIf it is irregular, the angles and sides would not all be congruent. PTS: 1 DIF: Basic REF: Lesson 1-6 OBJ: 1-6.2 Name polygons. NAT: NCTM ME.2 TOP: Name polygons. KEY: Polygons | Name Polygons 31. ANS: D Suppose the line containing each side is drawn. If any of the lines contain any point in the interior of the polygon, then it is concave. Otherwise it is convex. A convex polygon in which all the sides are congruent and all the angles are congruent is called a regular polygon. FeedbackAIf it is regular, the angles and sides would all be congruent.BIf it is concave, lines drawn from the segments would pass through the polygon.CCount the number of sides.DCorrect! PTS: 1 DIF: Average REF: Lesson 1-6 OBJ: 1-6.2 Name polygons. NAT: NCTM ME.2 TOP: Name polygons. KEY: Polygons | Name Polygons 32. ANS: D Suppose the line containing each side is drawn. If any of the lines contain any point in the interior of the polygon, then it is concave. Otherwise it is convex. A convex polygon in which all the sides are congruent and all the angles are congruent is called a regular polygon. FeedbackAIf it is regular the angles and sides would all be congruent.BIf it is concave, lines drawn from the segments would pass through the polygon.CCount the number of sides.DCorrect! PTS: 1 DIF: Average REF: Lesson 1-6 OBJ: 1-6.2 Name polygons. NAT: NCTM ME.2 TOP: Name polygons. KEY: Polygons | Name Polygons 33. ANS: A Perimeter is the sum of the sides. FeedbackACorrect!BCheck your math.CDid you add all three sides?DWhat is the sum of the three sides? PTS: 1 DIF: Average REF: Lesson 1-6 OBJ: 1-6.3 Find perimeter of two-dimensional figures. NAT: NCTM PS.1 | NCTM PS.2 | NCTM PS.3 TOP: Find the perimeters of polygons. KEY: Perimeter | Polygons 34. ANS: D Perimeter is the sum of the sides. FeedbackAWhat is the value of t?BDid you write and solve an equation?CCheck your math.DCorrect! PTS: 1 DIF: Average REF: Lesson 1-6 OBJ: 1-6.3 Find perimeter of two-dimensional figures. NAT: NCTM PS.1 | NCTM PS.2 | NCTM PS.3 TOP: Find the perimeters of polygons. KEY: Perimeter | Polygons 35. ANS: A The circumference C of a circle is the distance around the circle.  FeedbackACorrect!BYou need to multiply by 2.CUse the correct formula.DYou have calculated the area. PTS: 1 DIF: Average REF: Lesson 1-6 OBJ: 1-6.4 Find circumference of circles. NAT: NCTM GM.1 TOP: Find circumference of circles. KEY: Circumference | Circles 36. ANS: A The area of a rectangle is the product of its length and width.  FeedbackACorrect!BYou need to multiply not add.CPlace the decimal in the correct position.DYou have calculated the perimeter. PTS: 1 DIF: Basic REF: Lesson 1-6 OBJ: 1-6.5 Find area of two-dimensional figures. NAT: NCTM GM.1 TOP: Find area of two-dimensional figures. KEY: Area | Two-Dimensional Figures 37. ANS: A The area of a circle is the number of square units needed to cover a surface.  FeedbackACorrect!BUse the correct formula.CYou have calculated the circumference.DYou have multiplied by an additional term. PTS: 1 DIF: Basic REF: Lesson 1-6 OBJ: 1-6.5 Find area of two-dimensional figures. NAT: NCTM GM.1 TOP: Find area of two-dimensional figures. KEY: Area | Two-Dimensional Figures 38. ANS: B The set of all points in space that are a given distance from a given point is called a sphere. It is the three-dimensional equivalent of a circle. FeedbackAA cone has a circular base and a vertex.BCorrect!CA cylinder has two circular bases.DA prism has two congruent polygons for bases. PTS: 1 DIF: Basic REF: Lesson 1-7 OBJ: 1-7.1 Identify three-dimensional figures. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify three-dimensional figures. KEY: Three-Dimensional Figures 39. ANS: C This solid is a cylinder. The bases of a cylinder are circles. In this cylinder, the circular bases are centered at points A and B, thus the correct answer is  and . FeedbackAThe bases of a cylinder are circles, not segments.BThe bases of a cylinder are circles, not segments.CCorrect!DThose are the wrong centers for the circular bases. PTS: 1 DIF: Basic REF: Lesson 1-7 OBJ: 1-7.1 Identify three-dimensional figures. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify three-dimensional figures. KEY: Three-Dimensional Figures 40. ANS: A The edges of a solid are the line segments formed by the intersection of the faces. This figure has 12 such segments: four on top, four in the middle and four on the bottom. FeedbackACorrect!BThose are only the edges on the top of the solid. There are eight more.CThose are only the edges on the bottom of the solid. There are eight more.DThose are only the edges in the middle of the solid. There are eight more. PTS: 1 DIF: Basic REF: Lesson 1-7 OBJ: 1-7.1 Identify three-dimensional figures. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify and use three-dimensional figures. KEY: Three-Dimensional Figures 41. ANS: A A face of a solid is a flat surface. This solid contains five such surfaces: three lateral rectangles and two triangular bases. FeedbackACorrect!BThere is one more face on the bottom of the solid.CThe bases of the solid are also faces.DThere are three more faces besides the two base triangles. PTS: 1 DIF: Basic REF: Lesson 1-7 OBJ: 1-7.1 Identify three-dimensional figures. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify three-dimensional figures. KEY: Three-Dimensional Figures 42. ANS: A Start with 1. Add, subtract, or multiply the same number to each number to get the next one. FeedbackACorrect!BWhat operations are involved?CDidnt you carry the conjecture too far?DCheck your math. PTS: 1 DIF: Basic REF: Lesson 2-1 OBJ: 2-1.1 Make conjectures based on inductive reasoning. NAT: NCTM RP.2 TOP: Make conjectures based on inductive reasoning. KEY: Inductive Reasoning | Conjectures 43. ANS: A Concave polygons must be irregular. This means all sides and angles are not congruent. FeedbackACorrect!BWhat is the definition of concave?CIs that counterexample correct?DWhat is the definition of concave? PTS: 1 DIF: Basic REF: Lesson 2-1 OBJ: 2-1.2 Find counterexamples. NAT: NCTM RP.3 TOP: Find counterexamples. KEY: Counterexamples 44. ANS: C Angles are congruent only if their measures are equal. Point B may be closer to line AD or line DC so the measures would not be equal. FeedbackAWhat is the definition of congruent?BWhat is the definition of congruent?CCorrect!DWould that be a counterexample? PTS: 1 DIF: Basic REF: Lesson 2-1 OBJ: 2-1.2 Find counterexamples. NAT: NCTM RP.3 TOP: Find counterexamples. KEY: Counterexamples 45. ANS: D Because m is squared in the example, m could be positive or negative. FeedbackASubtract 6 from both sides.BWhat about negative numbers?CSubtract 6 from both sides.DCorrect! PTS: 1 DIF: Basic REF: Lesson 2-1 OBJ: 2-1.2 Find counterexamples. NAT: NCTM RP.3 TOP: Find counterexamples. KEY: Counterexamples 46. ANS: B Coplanar points always lie in the same plane. Three points are always coplanar but four are not. FeedbackAWhat does coplanar mean?BCorrect!CWhat does coplanar mean?DWould the points have to be in the same plane? PTS: 1 DIF: Basic REF: Lesson 2-1 OBJ: 2-1.2 Find counterexamples. NAT: NCTM RP.3 TOP: Find counterexamples. KEY: Counterexamples 47. ANS: C If two angles are supplementary their measures total 180. Either both are right or one is obtuse and the other acute. FeedbackAWhat is the definition of supplementary?BWhat is the definition of supplementary?CCorrect!DWhat is the definition of supplementary? PTS: 1 DIF: Basic REF: Lesson 2-1 OBJ: 2-1.2 Find counterexamples. NAT: NCTM RP.3 TOP: Find counterexamples. KEY: Counterexamples 48. ANS: D Unless there are specific angle measures mentioned, even though the angles in the picture may look congruent you cannot assume that they are congruent. FeedbackAWhat is the definition of congruent?BWhat is the definition of congruent?CWhat is the definition of congruent?DCorrect! PTS: 1 DIF: Basic REF: Lesson 2-1 OBJ: 2-1.2 Find counterexamples. NAT: NCTM RP.3 TOP: Find counterexamples. KEY: Counterexamples 49. ANS: B Even though they have a common point, the two segments do not have to be on the same line. FeedbackAWhat is the definition of midpoint?BCorrect!CWhat is the definition of midpoint?DWhat is the definition of midpoint? PTS: 1 DIF: Basic REF: Lesson 2-1 OBJ: 2-1.2 Find counterexamples. NAT: NCTM RP.3 TOP: Find counterexamples. KEY: Counterexamples 50. ANS: A Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. FeedbackACorrect!BWhat does statement r say?CAre four points always coplanar?DDoes a decagon have 12 sides? PTS: 1 DIF: Basic REF: Lesson 2-2 OBJ: 2-2.1 Determine truth values of conjunctions and disjunctions. NAT: NCTM RP.3 TOP: Determine truth values of conjunctions and disjunctions. KEY: Truth Values | Conjunctions | Disjunctions 51. ANS: D Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is . The symbol for logical or is . FeedbackAWhat is the symbol for logical and?BAre four points always coplanar?CWhat is the symbol for logical and?DCorrect! PTS: 1 DIF: Average REF: Lesson 2-2 OBJ: 2-2.1 Determine truth values of conjunctions and disjunctions. NAT: NCTM RP.3 TOP: Determine truth values of conjunctions and disjunctions. KEY: Truth Values | Conjunctions | Disjunctions 52. ANS: B Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is . The symbol for logical or is . FeedbackAWhat is the symbol for logical or?BCorrect!CHow many sides does a decagon have?DWhat is the symbol for logical or? PTS: 1 DIF: Average REF: Lesson 2-2 OBJ: 2-2.1 Determine truth values of conjunctions and disjunctions. NAT: NCTM RP.3 TOP: Determine truth values of conjunctions and disjunctions. KEY: Truth Values | Conjunctions | Disjunctions 53. ANS: A Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is . The symbol for logical or is . FeedbackACorrect!BWhat is the measure of a right angle?CHow many sides does a decagon have?DWhat is the measure of a right angle? PTS: 1 DIF: Average REF: Lesson 2-2 OBJ: 2-2.1 Determine truth values of conjunctions and disjunctions. NAT: NCTM RP.3 TOP: Determine truth values of conjunctions and disjunctions. KEY: Truth Values | Conjunctions | Disjunctions 54. ANS: D Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is . The symbol for logical or is . FeedbackAHow many sides does a decagon have?BWhat is the symbol for logical and?CWhat is the symbol for logical and?DCorrect! PTS: 1 DIF: Average REF: Lesson 2-2 OBJ: 2-2.1 Determine truth values of conjunctions and disjunctions. NAT: NCTM RP.3 TOP: Determine truth values of conjunctions and disjunctions. KEY: Truth Values | Conjunctions | Disjunctions 55. ANS: A Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is . The symbol for logical or is . FeedbackACorrect!BAre four points always coplanar?CWhat is the symbol for logical and?DWhat is the symbol for logical and? PTS: 1 DIF: Average REF: Lesson 2-2 OBJ: 2-2.1 Determine truth values of conjunctions and disjunctions. NAT: NCTM RP.3 TOP: Determine truth values of conjunctions and disjunctions. KEY: Truth Values | Conjunctions | Disjunctions 56. ANS: C The first statement column in a truth table contains half Ts, half Fs, grouped together. The second statement column in a truth table contains the same, but they are grouped by half the number that the first column was. The third statement column contains the same but they are grouped by half the number that the second column was. Use the truth values of the first three columns to determine the truth values for the last three columns. The symbol for not is . The symbol for logical and is . FeedbackACheck the values for the last column carefully.BCheck the values for the last column carefully.CCorrect!DDo your statement columns show every possible T and F combination? PTS: 1 DIF: Average REF: Lesson 2-2 OBJ: 2-2.2 Construct truth tables. NAT: NCTM RP.3 TOP: Construct truth tables. KEY: Truth Tables 57. ANS: C The inverse is negating both the hypothesis and conclusion of the conditional.  FeedbackARemember .BRemember .CCorrect!DIs that the converse? PTS: 1 DIF: Average REF: Lesson 2-3 OBJ: 2-3.3 Write the inverse of if-then statements. NAT: NCTM RP.3 TOP: Write the inverse of if-then statements. KEY: Inverse | If-Then Statements 58. ANS: D The inverse is negating both the hypothesis and conclusion of the conditional.  FeedbackAIs that the converse?BRemember .CRemember .DCorrect! PTS: 1 DIF: Average REF: Lesson 2-3 OBJ: 2-3.3 Write the inverse of if-then statements. NAT: NCTM RP.3 TOP: Write the inverse of if-then statements. KEY: Inverse | If-Then Statements 59. ANS: B The inverse is negating both the hypothesis and conclusion of the conditional.  FeedbackARemember .BCorrect!CRemember .DRemember . PTS: 1 DIF: Average REF: Lesson 2-3 OBJ: 2-3.3 Write the inverse of if-then statements. NAT: NCTM RP.3 TOP: Write the inverse of if-then statements. KEY: Inverse | If-Then Statements 60. ANS: A In the contrapositive you negate both the hypothesis and conclusion of the converse statement.  FeedbackACorrect!BIs that the inverse?CRemember .DRemember . PTS: 1 DIF: Basic REF: Lesson 2-3 OBJ: 2-3.4 Write the contrapositive of if-then statements. NAT: NCTM RP.1 TOP: Write the contrapositive of if-then statements. KEY: Contrapositive | If-Then Statements 61. ANS: D In the contrapositive you negate both the hypothesis and conclusion of the converse statement.  FeedbackARemember .BRemember .CRemember .DCorrect! PTS: 1 DIF: Average REF: Lesson 2-3 OBJ: 2-3.4 Write the contrapositive of if-then statements. NAT: NCTM RP.1 TOP: Write the contrapositive of if-then statements. KEY: Contrapositive | If-Then Statements 62. ANS: C In the contrapositive you negate both the hypothesis and conclusion of the converse statement.  FeedbackAIs this true?BRemember .CCorrect!DRemember . PTS: 1 DIF: Average REF: Lesson 2-3 OBJ: 2-3.4 Write the contrapositive of if-then statements. NAT: NCTM RP.1 TOP: Write the contrapositive of if-then statements. KEY: Contrapositive | If-Then Statements 63. ANS: B Postulates: 1. Through any two points, there is exactly one line. 2. Through any three points not on the same line, there is exactly one plane. 3. A line contains at least two points. 4. A plane contains at least three points not on the same line. 5. If two points lie in a plane, then the entire line containing those points lies in that plane. 6. If two lines intersect, then their intersection is exactly one point. 7. If two planes intersect, then their intersection is a line. FeedbackADoes that apply?BCorrect!CIs that a postulate?DDoes that fit the situation? PTS: 1 DIF: Average REF: Lesson 2-5 OBJ: 2-5.1 Identify and use basic postulates about points, lines, and planes. NAT: NCTM RP.1 TOP: Identify and use basic postulates about points, lines, and planes. KEY: Points | Lines | Planes 64. ANS: C Postulates: 1. Through any two points, there is exactly one line. 2. Through any three points not on the same line, there is exactly one plane. 3. A line contains at least two points. 4. A plane contains at least three points not on the same line. 5. If two points lie in a plane, then the entire line containing those points lies in that plane. 6. If two lines intersect, then their intersection is exactly one point. 7. If two planes intersect, then their intersection is a line. FeedbackAIs that a postulate?BDoes that fit the situation?CCorrect!DDoes that apply? PTS: 1 DIF: Average REF: Lesson 2-5 OBJ: 2-5.1 Identify and use basic postulates about points, lines, and planes. NAT: NCTM RP.1 TOP: Identify and use basic postulates about points, lines, and planes. KEY: Points | Lines | Planes 65. ANS: A Planes that intersect have a common line. FeedbackACorrect!BThis plane has four lines to intersect with other planes.CDo they all intersect plane CDI in a line?DThis plane has four lines to intersect with other planes. PTS: 1 DIF: Basic REF: Lesson 3-1 OBJ: 3-1.1 Identify the relationships between two lines or two planes. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify the relationships between two lines or two planes. KEY: Relationship Between Two Lines | Relationship Between Two Planes 66. ANS: B Coplanar segments that do not intersect are parallel. FeedbackAAre those parallel to ?BCorrect!CAre those all of the segments parallel to ?DAre those all of the segments parallel to ? PTS: 1 DIF: Basic REF: Lesson 3-1 OBJ: 3-1.1 Identify the relationships between two lines or two planes. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify the relationships between two lines or two planes. KEY: Relationship Between Two Lines | Relationship Between Two Planes 67. ANS: B Planes intersect in a line. FeedbackADo they all intersect plane CHG in a line?BCorrect!CIs that all?DDo they all intersect plane CHG in a line? PTS: 1 DIF: Average REF: Lesson 3-1 OBJ: 3-1.1 Identify the relationships between two lines or two planes. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify the relationships between two lines or two planes. KEY: Relationship Between Two Lines | Relationship Between Two Planes 68. ANS: A Skew lines do not intersect and are not coplanar. FeedbackACorrect!BSkew lines do not intersect.CSkew lines are not coplanar.DSkew lines are not coplanar. PTS: 1 DIF: Average REF: Lesson 3-1 OBJ: 3-1.1 Identify the relationships between two lines or two planes. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify the relationships between two lines or two planes. KEY: Relationship Between Two Lines | Relationship Between Two Planes 69. ANS: A Skew lines do not intersect and are not coplanar. FeedbackACorrect!BSkew lines do not intersect.CSkew lines are not coplanar.DSkew lines are not coplanar. PTS: 1 DIF: Average REF: Lesson 3-1 OBJ: 3-1.1 Identify the relationships between two lines or two planes. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify the relationships between two lines or two planes. KEY: Relationship Between Two Lines | Relationship Between Two Planes 70. ANS: B Planes intersect in a line. FeedbackADo they all intersect plane CHG in a line?BCorrect!CIs that all?DDo they all intersect plane CHG in a line? PTS: 1 DIF: Average REF: Lesson 3-1 OBJ: 3-1.1 Identify the relationships between two lines or two planes. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify the relationships between two lines or two planes. KEY: Relationship Between Two Lines | Relationship Between Two Planes 71. ANS: C Coplanar segments that do not intersect are parallel. FeedbackAParallel lines do not intersect.BParallel lines are coplanar.CCorrect!DThose segments are parallel to which line? PTS: 1 DIF: Basic REF: Lesson 3-1 OBJ: 3-1.1 Identify the relationships between two lines or two planes. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify the relationships between two lines or two planes. KEY: Relationship Between Two Lines | Relationship Between Two Planes 72. ANS: D A line that intersects two or more lines in a plane at different points is called a transversal. FeedbackAWhat about line p?BYou need every combination of the lines.CWhat is the definition of transversal?DCorrect! PTS: 1 DIF: Basic REF: Lesson 3-1 OBJ: 3-1.2 Name angles formed by a pair of lines and a transversal. NAT: NCTM GM.1 | NCTM GM.1b TOP: Name angles formed by a pair of lines and a transversal. KEY: Transversals | Two Lines and a Transversal | Angles 73. ANS: A A line that intersects two or more lines in a plane at different points is called a transversal. FeedbackACorrect!BWhat is the definition of transversal?CYou need every combination of lines.DYou need every combination of the lines. PTS: 1 DIF: Average REF: Lesson 3-1 OBJ: 3-1.2 Name angles formed by a pair of lines and a transversal. NAT: NCTM GM.1 | NCTM GM.1b TOP: Name angles formed by a pair of lines and a transversal. KEY: Transversals | Two Lines and a Transversal | Angles 74. ANS: D Extend v to intersect with p. This creates a linear pair at point S with angles measuring  (given) and 61. The angles formed by the intersection of v and p (also linear pairs) measure  (corresponding angles) and 55 with the latter being one of the interior angles of the triangle formed by t, p, and v. Since the sum of the angles of a triangle is 180, the angle that is vertical to 1 is 64, thus making 1 64 as well. FeedbackAExtend v as a transversal of q and p.BExtend v as a transversal of q and p.CExtend v as a transversal of q and p.DCorrect! PTS: 1 DIF: Average REF: Lesson 3-2 OBJ: 3-2.2 Use algebra to find angle measures. NAT: NCTM AL.4a | NCTM GM.2 | NCTM GM.2a TOP: Use algebra to find angle measures. KEY: Angles | Angle Measures 75. ANS: C The formula for slope is . If the slopes are the same, the lines are parallel. If the product of the two slopes is 1, the lines are perpendicular. FeedbackAParallel slopes are the same and perpendicular ones are opposite reciprocals.BParallel slopes are the same and perpendicular ones are opposite reciprocals.CCorrect! PTS: 1 DIF: Average REF: Lesson 3-3 OBJ: 3-3.2 Use slope to identify parallel and perpendicular lines. NAT: NCTM AL.2 | NCTM AL.2c | NCTM RE.2 TOP: Use slope to identify parallel lines and perpendicular lines. KEY: Parallel Lines | Perpendicular Lines | Slope 76. ANS: B The slope-intercept form is . Point b is the point at which . FeedbackAWhat is the y-intercept?BCorrect!CWhat is the slope of the line?DRemember y = mx + b. PTS: 1 DIF: Average REF: Lesson 3-4 OBJ: 3-4.1 Write an equation of a line given information about its graph. NAT: NCTM AL.2 TOP: Write an equation of a line given information about its graph. KEY: Equation of Lines | Graphs 77. ANS: D The point-slope form is . Point  is a point through which the line passes. FeedbackAIs that point-slope form?BWhat is the slope?CRemember the point is (x1, y1).DCorrect! PTS: 1 DIF: Average REF: Lesson 3-4 OBJ: 3-4.2 Solve problems by writing equations. NAT: NCTM GM.1 | NCTM GM.1b TOP: Solve problems by writing equations. KEY: Solve Problems | Write Equations 78. ANS: A The point-slope form is . Point  is a point through which the line passes. FeedbackACorrect!BWhat are x1 and y1?CBe careful with sign rules?DIs that point-slope form? PTS: 1 DIF: Average REF: Lesson 3-4 OBJ: 3-4.2 Solve problems by writing equations. NAT: NCTM GM.1 | NCTM GM.1b TOP: Solve problems by writing equations. KEY: Solve Problems | Write Equations 79. ANS: C The point-slope form is . Point  is a point through which the line passes. FeedbackAIs that point-slope form?BRemember the point is (x1, y1).CCorrect!DBe careful with signs. PTS: 1 DIF: Average REF: Lesson 3-4 OBJ: 3-4.2 Solve problems by writing equations. NAT: NCTM GM.1 | NCTM GM.1b TOP: Solve problems by writing equations. KEY: Solve Problems | Write Equations 80. ANS: C Postulates and theorems: If corresponding angles are congruent, then lines are parallel. If given a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line. If alternate exterior angles are congruent, then lines are parallel. If consecutive interior angles are supplementary, then lines are parallel. If alternate interior angles are congruent, then lines are parallel. If two lines are perpendicular to the same line, then lines are parallel. FeedbackAWhat kind of angles are those?BWhat kind of angles are those?CCorrect!DWhich lines are parallel? PTS: 1 DIF: Average REF: Lesson 3-5 OBJ: 3-5.1 Recognize angle conditions that occur with parallel lines. NAT: NCTM GM.1b | NCTM GM.1c | NCTM RP.3 TOP: Recognize angle conditions that occur with parallel lines. KEY: Angles | Parallel Lines 81. ANS: B The slope of a line p perpendicular to m has the negative reciprocal to the equation of line m. The slope of line m is , which is 0. This is a horizontal line. The perpendicular line, then would be a vertical line, , going through point P. The point on m where line p intersects it would be . Use the Distance Formula to find the distance from point P to the point on m that intersects line p.  FeedbackARemember it is (x, y).BCorrect!CYou want the distance to line m.DYou want the distance to line m. PTS: 1 DIF: Basic REF: Lesson 3-6 OBJ: 3-6.1 Find the distance between a point and a line. NAT: NCTM GM.2 | NCTM GM.2a TOP: Find the distance between a point and a line. KEY: Distance | Distance Between a Point and a Line 82. ANS: C The slope of a line perpendicular to each has the negative reciprocal to the equation of one of the lines. The perpendicular line containing the y-intercept would be . You need to find a common point for the two lines, so set the equations equal to each other.  Use the Distance Formula from that common point to the y-intercept of the first line.  FeedbackAConstruct a perpendicular line and find the intersection point on each parallel line.BConstruct a perpendicular line and find the intersection point on each parallel line.CCorrect!DConstruct a perpendicular line and find the intersection point on each parallel line. PTS: 1 DIF: Average REF: Lesson 3-6 OBJ: 3-6.2 Find the distance between parallel lines. NAT: NCTM PS.1 | NCTM PS.2 | NCTM PS.3 TOP: Find the distance between parallel lines. KEY: Distance | Parallel Lines | Distance Between Parallel Lines 83. ANS: B An acute triangle has 3 acute angles. An obtuse triangle has one obtuse angle. A right triangle has one right angle. An equiangular triangle has at least 2 congruent sides. FeedbackACheck for congruent sides and measure angles.BCorrect!CCheck for congruent sides and measure angles.DCheck for congruent sides and measure angles. PTS: 1 DIF: Basic REF: Lesson 4-1 OBJ: 4-1.1 Identify and classify triangles by angles. NAT: NCTM GM.1 | NCTM GM.1a TOP: Identify and classify triangles by angles. KEY: Triangles | Classify Triangles 84. ANS: D Use the Distance Formula to find the lengths of the sides.  If  or  or , then the triangle is isosceles. If , then the triangle is equilateral. If neither of the above, the triangle is scalene. FeedbackAUse the distance formula to find the lengths of the sides.BWhat are the lengths of the sides?CDid you use the distance formula?DCorrect! PTS: 1 DIF: Average REF: Lesson 4-1 OBJ: 4-1.2 Identify and classify triangles by sides. NAT: NCTM GM.1 | NCTM GM.1b TOP: Identify and classify triangles by sides. KEY: Triangles | Classify Triangles 85. ANS: B The Angle Sum Theorem states that the sum of the measures of the angles of a triangle is 180. FeedbackADid you use the Angle Sum Theorem.BCorrect!CUse the Angle Sum Theorem.DUse the Angle Sum Theorem. PTS: 1 DIF: Average REF: Lesson 4-2 OBJ: 4-2.1 Apply the Angle Sum Theorem. NAT: NCTM GM.1 | NCTM GM.1b TOP: Apply the Angle Sum Theorem. KEY: Angle Sum Theorem 86. ANS: A The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. FeedbackACorrect!BWhat is the sum of the measures of the angles in a triangle?CDid you use the Exterior Angle Theorem?DUse the Exterior Angle Theorem. PTS: 1 DIF: Average REF: Lesson 4-2 OBJ: 4-2.2 Apply the Exterior Angle Theorem. NAT: NCTM GM.1 | NCTM GM.1b TOP: Apply the Exterior Angle Theorem. KEY: Exterior Angle Theorem 87. ANS: D The letters naming the triangles correspond to the congruent vertices of the two triangles in the same order. FeedbackABe careful with the order of the vertices.BAre the vertices in the correct order?CThe letters naming the triangles correspond to the congruent vertices of the two triangles.DCorrect! PTS: 1 DIF: Average REF: Lesson 4-3 OBJ: 4-3.2 Identify congruent transformations. NAT: NCTM GM.1 | NCTM GM.1b TOP: Identify congruent transformations. KEY: Transformations | Congruence Transformations 88. ANS: D If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the triangles are congruent. FeedbackAUse the SSS Postulate.BCheck your math.CHow do you determine if two triangles are congruent?DCorrect! PTS: 1 DIF: Average REF: Lesson 4-4 OBJ: 4-4.1 Use the SSS Postulate to test for triangle congruence. NAT: NCTM GM.1 | NCTM GM.1b TOP: Use the SSS Postulate to test for triangle congruence. KEY: SSS Postulate | Congruent Triangles 89. ANS: A   FeedbackACorrect!BWhat do you know about the sides of an equilateral triangle?CHow many degrees is each angle of an equilateral triangle?DDid you add or subtract when solving for y? PTS: 1 DIF: Average REF: Lesson 4-6 OBJ: 4-6.2 Use the properties of equilateral triangles. NAT: NCTM GM.2 | NCTM GM.2a TOP: Use the properties of equilateral triangles. KEY: Equilateral Triangles 90. ANS: D   FeedbackADid you use the Pythagorean Theorem?BDid you add instead of subtract?CCheck your math.DCorrect! PTS: 1 DIF: Average REF: Lesson 4-6 OBJ: 4-6.2 Use the properties of equilateral triangles. NAT: NCTM GM.2 | NCTM GM.2a TOP: Use the properties of equilateral triangles. KEY: Equilateral Triangles 91. ANS: D   FeedbackADid you use the Pythagorean Theorem correctly?BCheck your math.CShould you have subtracted?DCorrect! PTS: 1 DIF: Average REF: Lesson 4-6 OBJ: 4-6.2 Use the properties of equilateral triangles. NAT: NCTM GM.2 | NCTM GM.2a TOP: Use the properties of equilateral triangles. KEY: Equilateral Triangles 92. ANS: B PTS: 1 DIF: Basic REF: Lesson 4-7 OBJ: 4-7.1 Identify reflections, translations, and rotations. NAT: NCTM GM.2 | NCTM GM.3 TOP: Congruence transformations. KEY: congruence transformation 93. ANS: B 1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible. FeedbackALook at your labels.BCorrect!CWhich sides are congruent?DWhich sides are congruent? PTS: 1 DIF: Basic REF: Lesson 4-8 OBJ: 4-8.1 Position and label triangles for use in coordinate proofs. NAT: NCTM PS.1 | NCTM PS.2 | NCTM PS.3 TOP: Position and label triangles for use in coordinate proofs. KEY: Proofs | Coordinate Proofs 94. ANS: A 1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible. FeedbackACorrect!BWhat is the base?CWhat is the base of that triangle?DLook at your labels. PTS: 1 DIF: Average REF: Lesson 4-8 OBJ: 4-8.1 Position and label triangles for use in coordinate proofs. NAT: NCTM PS.1 | NCTM PS.2 | NCTM PS.3 TOP: Position and label triangles for use in coordinate proofs. KEY: Proofs | Coordinate Proofs 95. ANS: D 1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible. FeedbackAWhat segment is the hypotenuse?BLook at your labels.CWhich leg is 4a units long?DCorrect! PTS: 1 DIF: Average REF: Lesson 4-8 OBJ: 4-8.1 Position and label triangles for use in coordinate proofs. NAT: NCTM PS.1 | NCTM PS.2 | NCTM PS.3 TOP: Position and label triangles for use in coordinate proofs. KEY: Proofs | Coordinate Proofs 96. ANS: D 1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible. FeedbackAWhich segment is the base?BWhere does the triangle belong?CLook at your labels.DCorrect! PTS: 1 DIF: Basic REF: Lesson 4-8 OBJ: 4-8.1 Position and label triangles for use in coordinate proofs. NAT: NCTM PS.1 | NCTM PS.2 | NCTM PS.3 TOP: Position and label triangles for use in coordinate proofs. KEY: Proofs | Coordinate Proofs 97. ANS: A 1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible. FeedbackACorrect!BLook at your placement.CHow tall is the triangle?DHow tall is the triangle? PTS: 1 DIF: Average REF: Lesson 4-8 OBJ: 4-8.1 Position and label triangles for use in coordinate proofs. NAT: NCTM PS.1 | NCTM PS.2 | NCTM PS.3 TOP: Position and label triangles for use in coordinate proofs. KEY: Proofs | Coordinate Proofs 98. ANS: A If  is an altitude, . The measures of the angles of every triangle add up to 180. FeedbackACorrect!BWhich angle measures add up to 180?CWhich angles must measure 90?DCheck your math. PTS: 1 DIF: Average REF: Lesson 5-2 OBJ: 5-2.1 Use altitudes in triangles. NAT: NCTM GM.1 | NCTM GM.1a TOP: Use altitudes in triangles. KEY: Altitudes | Triangles 99. ANS: D The sum of the lengths of any two sides must be greater than the third. FeedbackADid you check all the sums?BAdd two sides and compare to the third.CAdd two sides and compare to the third.DCorrect! PTS: 1 DIF: Basic REF: Lesson 5-5 OBJ: 5-5.1 Apply the Triangle Inequality Theorem. NAT: NCTM GM.2 | NCTM GM.2a TOP: Apply the Triangle Inequality Theorem. KEY: Triangles Inequality Theorem 100. ANS: C The sum of the lengths of any two sides must be greater than the third. FeedbackADid you check all the sums?BAdd two sides and compare to the third.CCorrect!DAdd two sides and compare to the third. PTS: 1 DIF: Average REF: Lesson 5-5 OBJ: 5-5.1 Apply the Triangle Inequality Theorem. NAT: NCTM GM.2 | NCTM GM.2a TOP: Apply the Triangle Inequality Theorem. KEY: Triangles Inequality Theorem SHORT ANSWER 101. ANS: No; the average daily temperature for City G could be as low as  or as high as  The average daily temperature for City H could be as low as  or as high as  The difference in temperature could be as high as  An absolute error of 0.5 is acceptable. Add and subtract the absolute error from the given measurement to get the high and low values respectively. PTS: 1 DIF: Advanced REF: Lesson 1-2 OBJ: 1-2.4 Solve multi-step problems. NAT: NCTM ME.2 | NCTM ME.2a | NCTM NO.1 TOP: Solve multi-step problems. KEY: Solve multi-step problems. 102. ANS:  The midpoint of a segment is the point halfway between the endpoints of the segment. The coordinates of the midpoint of a segment with endpoints that have the coordinates  and  are  PTS: 1 DIF: Advanced REF: Lesson 1-3 OBJ: 1-3.4 Solve multi-step problems. NAT: NCTM GM.2 | NCTM GM.2a | NCTM ME.1 TOP: Solve multi-step problems. KEY: Solve multi-step problems. 103. ANS: 62, 28 Calculate the angle of reflection by using the relation . Also, r and  are complementary i.e.  PTS: 1 DIF: Basic REF: Lesson 1-5 OBJ: 1-5.2 Solve multi-step problems. NAT: NCTM GM.1 | NCTM GM.1a TOP: Solve multi-step problems. KEY: Solve multi-step problems. 104. ANS:    Calculate the angle of reflection by using the relation . Also, i and  are complementary i.e.  PTS: 1 DIF: Advanced REF: Lesson 1-5 OBJ: 1-5.2 Solve multi-step problems. NAT: NCTM GM.1 | NCTM GM.1a TOP: Solve multi-step problems. KEY: Solve multi-step problems. 105. ANS: 3.8 in. Here, the perimeter of the square is equal to the circumference of the circular loop. Use this relationship to find the maximum radius of the loop. PTS: 1 DIF: Advanced REF: Lesson 1-6 OBJ: 1-6.6 Solve multi-step problems. NAT: NCTM GM.1 | NCTM GM.1a | NCTM ME.2 | NCTM PS.1 | NCTM PS.2 | NCTM PS.3 TOP: Solve multi-step problems. KEY: Solve multi-step problems. 106. ANS: 19.1 cm Here, the perimeter of the square painting is equal to the circumference of the circular picture frame. Use this relationship to find the maximum radius of the frame. PTS: 1 DIF: Average REF: Lesson 1-6 OBJ: 1-6.6 Solve multi-step problems. NAT: NCTM GM.1 | NCTM GM.1a | NCTM ME.2 | NCTM PS.1 | NCTM PS.2 | NCTM PS.3 TOP: Solve multi-step problems. KEY: Solve multi-step problems. 107. ANS: 52.7  The surface area T, of a triangular prism is the sum of the areas of each face of a solid. ; where P is the perimeter of the base, h is the height, and B is the area of the base. PTS: 1 DIF: Advanced REF: Lesson 1-7 OBJ: 1-7.4 Solve multi-step problems. NAT: NCTM GM.1 | NCTM GM.1a | NCTM GM.4 | NCTM GM.4a | NCTM GM.4b | NCTM GM.1 TOP: Solve multi-step problems. KEY: Solve multi-step problems. 108. ANS: Sample: Two adjacent angles formed by two intersecting lines are not vertical angles. True. PTS: 1 DIF: Average REF: Lesson 2-3 OBJ: 2-3.4 Write the contrapositive of if-then statements. NAT: NCTM RP.1 TOP: Write the contrapositive of if-then statements. KEY: Contrapositive | If-Then Statements 109. ANS: Sample: Noncongruent segments are not two segments having the same measure. True. PTS: 1 DIF: Average REF: Lesson 2-3 OBJ: 2-3.4 Write the contrapositive of if-then statements. NAT: NCTM RP.1 TOP: Write the contrapositive of if-then statements. KEY: Contrapositive | If-Then Statements 110. ANS: Sample: Given:  and  are adjacent angles. Prove: Point Q is in the interior of . Proof: By the definition of adjacent angles, the two angles have a common side . Since R is the common vertex, Q must be in the interior of .  PTS: 1 DIF: Basic REF: Lesson 2-5 OBJ: 2-5.2 Write paragraph proofs. NAT: NCTM RP.1 TOP: Write paragraph proofs. KEY: Proofs | Paragraph Proofs 111. ANS: Sample: Given: Isosceles triangle GHJ;  is a segment between points K and L on line KL; HG = JG. Prove:  Proof: Since they are linear pairs,  and . Therefore . Since the triangle is isosceles, . Subtracting the equal angles gives . By definition of congruent angles . PTS: 1 DIF: Average REF: Lesson 2-5 OBJ: 2-5.2 Write paragraph proofs. NAT: NCTM RP.1 TOP: Write paragraph proofs. KEY: Proofs | Paragraph Proofs 112. ANS: Sample: Given:  all intersect at point P;  and . Prove:  Proof:  and . If , by definition of congruent angles, . Substituting, . PTS: 1 DIF: Basic REF: Lesson 2-5 OBJ: 2-5.2 Write paragraph proofs. NAT: NCTM RP.1 TOP: Write paragraph proofs. KEY: Proofs | Paragraph Proofs 113. ANS: Sample: Given: Vertical isosceles triangles;  bisects ; . Prove:  Proof:  because vertical angles are congruent.  bisects , and by definition of a segment bisector, it bisects at the midpoint. Definition of a midpoint gives two equal segments, which by definition of congruence leads to . Since ,  by the AAS Theorem. PTS: 1 DIF: Basic REF: Lesson 4-5 OBJ: 4-5.2 Use the AAS Theorem to test for triangle congruence. NAT: NCTM GM.1 | NCTM GM.1a TOP: Use the AAS Theorem to test for triangle congruence. KEY: AAS Theorem | Congruent Triangles 114. ANS: Sample: Given: Regular hexagon ABCDFG;  each bisect the hexagon and meet at point H;  and . Prove:  Proof: StatementsReasons1.  and 1. Given2. 2. Definition of congruent segments3. , 3. Segment Addition Postulate4. 4. Substitution Property5. 5. Substitution Property6. 6. Reflexive Property7. 7. Subtraction Property8. 8. Definition of congruent segments PTS: 1 DIF: Average REF: Lesson 2-7 OBJ: 2-7.2 Write proofs involving segment congruence. NAT: NCTM GM.1c | NCTM RP.3 TOP: Write proofs involving segment congruence. KEY: Proofs | Congruent Segments 115. ANS: Sample: Given: .  ; ;  Prove:  Proof: StatementsReasons1. , , , 1. Given2.  2. Angle Addition Postulate3. 3. Substitution Property4. 4. Substitution Property5. 5. Reflexive Property6. 6. Subtraction Property PTS: 1 DIF: Average REF: Lesson 2-8 OBJ: 2-8.2 Write proofs involving congruent angles. NAT: NCTM GM.1c | NCTM RP.3 TOP: Write proofs involving congruent angles. KEY: Proofs | Congruent Angles 116. ANS: Sample: Given:  Prove:  Proof: StatementsReasons1. 1. Given2. , 2. Given3.  are right angles.3. Definition of perpendicular4. , 4. Definition of right angle5. 5. Substitution Property6. 6. Definition of congruent angles PTS: 1 DIF: Basic REF: Lesson 2-8 OBJ: 2-8.3 Write proofs involving right angles. NAT: NCTM PS.1 | NCTM PS.2 | NCTM PS.3 TOP: Write proofs involving right angles. KEY: Proofs | Right Angles 117. ANS: Sample: Given: Square GHJK Prove:  Proof: StatementsReasons1. GHJK is a square.1. Given2. 2. Definition of a square3. 3. Definition of a square4. 4. Reflexive Property5. 5. SSS Postulate PTS: 1 DIF: Basic REF: Lesson 4-4 OBJ: 4-4.1 Use the SSS Postulate to test for triangle congruence. NAT: NCTM GM.1 | NCTM GM.1b TOP: Use the SSS Postulate to test for triangle congruence. KEY: SSS Postulate | Congruent Triangles 118. ANS: Sample: Given: W is the midpoint of  and ; . Prove:  Proof: StatementsReasons1. W is the midpoint of .1. Given2. 2. Midpoint Theorem3. W is the midpoint of .3. Given4. 4. Midpoint Theoremt5. 5. Given6. 6. SSS Postulate PTS: 1 DIF: Average REF: Lesson 4-4 OBJ: 4-4.1 Use the SSS Postulate to test for triangle congruence. NAT: NCTM GM.1 | NCTM GM.1b TOP: Use the SSS Postulate to test for triangle congruence. KEY: SSS Postulate | Congruent Triangles 119. ANS: Sample: Given: M is the midpoint of  and . Prove:  Proof: StatementsReasons1. M is the midpoint of .1. Given2. 2. Midpoint Theorem3. M is the midpoint of .3. Given4. 4. Midpoint Theorem5. The polygon is a regular hexagon.5. Given6. 6. Definition of regular hexagon7. 7. SSS Postulate PTS: 1 DIF: Average REF: Lesson 4-4 OBJ: 4-4.1 Use the SSS Postulate to test for triangle congruence. NAT: NCTM GM.1 | NCTM GM.1b TOP: Use the SSS Postulate to test for triangle congruence. KEY: SSS Postulate | Congruent Triangles 120. ANS:  Find the number of people who joined the math club only, the number of people who joined theater only, and the number of people who joined neither math club nor theater. Plot all these calculated values together with the number of people who joined both on the Venn diagram to represent the data. PTS: 1 DIF: Average REF: Lesson 2-2 OBJ: 2-2.3 Solve multi-step problems. NAT: NCTM RP.3 TOP: Solve multi-step problems. KEY: Solve multi-step problems. 121. ANS:  Find the number of people who have been to Mexico only, the number of people who have been to Canada only, and the number of people who have been to neither Mexico nor Canada. Plot all these calculated values together with the number of people who have been to both Mexico and Canada on the Venn diagram to represent the data. PTS: 1 DIF: Advanced REF: Lesson 2-2 OBJ: 2-2.3 Solve multi-step problems. NAT: NCTM RP.3 TOP: Solve multi-step problems. KEY: Solve multi-step problems. 122. ANS: Sample answer: If a triangle has three acute angles, then it is an acute triangle; true. The converse of a conditional statement  exchanges the hypothesis and conclusion of the conditional. It is also known as  PTS: 1 DIF: Average REF: Lesson 2-3 OBJ: 2-3.5 Solve multi-step problems. NAT: NCTM RP.3 | NCTM RP.1 TOP: Solve multi-step problems. KEY: Solve multi-step problems. 123. ANS: Sample answer: Conditional statement: If a figure is a right triangle, then it has one right angle. Converse: If a triangle has one right angle, then it is a right triangle. A conditional statement is a statement that can be written in if-then form. The converse of a conditional statement  exchanges the hypothesis and conclusion of the conditional. It is also known as  PTS: 1 DIF: Average REF: Lesson 2-3 OBJ: 2-3.5 Solve multi-step problems. NAT: NCTM RP.3 | NCTM RP.1 TOP: Solve multi-step problems. KEY: Solve multi-step problems. 124. ANS: invalid Law of Detachment is a form of deductive reasoning which is used to draw conclusions from true conditional statements. In other words, if the conditional statement is true and the hypothesis is true, then according to the Law of Detachment the conclusion is also true. PTS: 1 DIF: Average REF: Lesson 2-4 OBJ: 2-4.2 Solve multi-step problems. NAT: NCTM GM.1 | NCTM GM.1a TOP: Solve multi-step problems. KEY: Solve multi-step problems. 125. ANS: then Emma goes swimming. A true conditional statement and a true hypothesis is given in the problem. Use the Law of Detachment to draw the conclusion. PTS: 1 DIF: Advanced REF: Lesson 2-4 OBJ: 2-4.2 Solve multi-step problems. NAT: NCTM GM.1 | NCTM GM.1a TOP: Solve multi-step problems. KEY: Solve multi-step problems. 126. ANS: He will have 6 different planes and 10 lines. Points that do not lie on the same line are noncollinear. Points that do not lie in the same plane are noncoplanar. PTS: 1 DIF: Average REF: Lesson 2-5 OBJ: 2-5.3 Solve multi-step problems. NAT: NCTM RP.1 TOP: Solve multi-step problems. KEY: Solve multi-step problems. 127. ANS:  If two angles are vertical angles, then they are congruent. PTS: 1 DIF: Advanced REF: Lesson 2-8 OBJ: 2-8.4 Solve multi-step problems. NAT: NCTM GM.1c | NCTM RP.3 | NCTM PS.1 | NCTM PS.2 | NCTM PS.3 TOP: Solve multi-step problems. KEY: Solve multi-step problems. 128. ANS: skew lines Lines that do not intersect and are not coplanar are called skew lines. PTS: 1 DIF: Advanced REF: Lesson 3-1 OBJ: 3-1.3 Solve multi-step problems. NAT: NCTM GM.1 | NCTM GM.1a | NCTM GM.1b TOP: Solve multi-step problems. KEY: Solve multi-step problems. 129. ANS: 3050 Calculate the rate of change. Multiply it by 4 and then add the product to the circulation number in 1997 to predict the circulation for 2001.  PTS: 1 DIF: Average REF: Lesson 3-3 OBJ: 3-3.3 Solve multi-step problems. NAT: NCTM AL.2 | NCTM AL.2c | NCTM RE.2 | NCTM GM.1b | NCTM GM.2 | NCTM GM.2a TOP: Solve multi-step problems. KEY: Solve multi-step problems. 130. ANS: Sample answer: 92.5 Find the rate of change. Multiply it by 8 and then add the product to the number of laptop computers used in 1998 to predict the number of laptop computers used in 2006.  PTS: 1 DIF: Advanced REF: Lesson 3-3 OBJ: 3-3.3 Solve multi-step problems. NAT: NCTM AL.2 | NCTM AL.2c | NCTM RE.2 | NCTM GM.1b | NCTM GM.2 | NCTM GM.2a TOP: Solve multi-step problems. KEY: Solve multi-step problems. 131. ANS:  The slope-intercept form of a linear equation is  where m is the slope of the line and b is the y-intercept. Use the point-slope form and either point to write the equation.   are the coordinates of any point on the line and  is the slope of the line. PTS: 1 DIF: Advanced REF: Lesson 3-4 OBJ: 3-4.3 Solve multi-step problems. NAT: NCTM AL.2 | NCTM GM.1 | NCTM GM.1b TOP: Solve multi-step problems. KEY: Solve multi-step problems. 132. ANS:  An obtuse triangle has one obtuse angle. PTS: 1 DIF: Average REF: Lesson 4-1 OBJ: 4-1.3 Solve multi-step problems. NAT: NCTM GM.1 | NCTM GM.1a | NCTM GM.1b TOP: Solve multi-step problems. KEY: Solve multi-step problems. 133. ANS: Given: PQRS is a quadrilateral. Prove:   Proof: StatementsReasons1. PQRS is a quadrilateral.1. Given2.  2. Angle Sum Theorem3. 3. Addition Property4. 4. Angle Addition Postulate5. 5. Substitution A two-column proof is a deductive argument that contains statements and reasons organized in two columns. The sum of the measures of the angles of a triangle is 180. PTS: 1 DIF: Advanced REF: Lesson 4-1 OBJ: 4-2.3 Solve multi-step problems. NAT: NCTM GM.1 | NCTM GM.1b TOP: Solve multi-step problems. KEY: Solve multi-step problems. 134. ANS: Sample: Given:  is isosceles; . Prove:  Proof:  PTS: 1 DIF: Average REF: Lesson 4-5 OBJ: 4-5.1 Use the ASA Postulate to test for triangle congruence. NAT: NCTM GM.1 | NCTM GM.1b TOP: Use the ASA Postulate to test for triangle congruence. KEY: ASA Postulate | Congruent Triangles 135. ANS: Sample: Given:  bisects ; . Prove:  Proof:  PTS: 1 DIF: Average REF: Lesson 4-5 OBJ: 4-5.1 Use the ASA Postulate to test for triangle congruence. NAT: NCTM GM.1 | NCTM GM.1b TOP: Use the ASA Postulate to test for triangle congruence. KEY: ASA Postulate | Congruent Triangles 136. ANS: Given:  Prove:   Proof: We are given that  so by definition of angle bisector,  It is given that  By the Reflexive Property,   by ASA. A paragraph proof is a deductive argument that contains statements and reasons organized in a paragraph. If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. PTS: 1 DIF: Basic REF: Lesson 4-5 OBJ: 4-5.3 Solve multi-step problems. NAT: NCTM GM.1 | NCTM GM.1b | NCTM GM.1a TOP: Solve multi-step problems. KEY: Solve multi-step problems. 137. ANS: Since T is the midpoint of PR,  As   because alternate interior angles are congruent. Also,  because vertical angles are congruent. So,  by ASA. If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. PTS: 1 DIF: Advanced REF: Lesson 4-5 OBJ: 4-5.3 Solve multi-step problems. NAT: NCTM GM.1 | NCTM GM.1b | NCTM GM.1a TOP: Solve multi-step problems. KEY: Solve multi-step problems. 138. ANS: Sample: Given:  is equilateral;.  bisects . Prove: T is the midpoint of . Proof: StatementsReasons1.  is equilateral.1. Given2. 2. Equilateral triangles are equiangular.3. 3. Definition of equilateral triangle4.  bisects .4. Given5. 5. Definition of angle bisector6. 6. ASA Postulate7. 7. CPCTC8. 8. Definition of congruence9. T is the midpoint of 9. Definition of midpoint PTS: 1 DIF: Basic REF: Lesson 4-6 OBJ: 4-6.3 Solve multi-step problems. NAT: NCTM GM.1 | NCTM GM.1a | NCTM GM.2 | NCTM GM.2a TOP: Use properties of equilateral triangles. KEY: Equilateral Triangles 139. ANS: Given:  is equilateral; . Prove:   Proof: StatementsReasons1. 1. Given2. 2. Definition of equilateral triangle3. 3. Given4. 4. Given5. 5. SAS6. 6. CPCTC7. 7. Isosceles Triangle Theorem A two-column proof is a deductive argument that contains statements and reasons organized in two columns. If two sides of a triangle are congruent, then the angles opposite those sides are congruent. PTS: 1 DIF: Average REF: Lesson 4-6 OBJ: 4-6.3 Solve multi-step problems. NAT: NCTM GM.1 | NCTM GM.1a | NCTM GM.2 | NCTM GM.2a TOP: Solve multi-step problems. KEY: Solve multi-step problems. 140. ANS: rotation PTS: 1 DIF: Average REF: Lesson 4-7 OBJ: 4-7.3 Solve multi-step problems. NAT: NCTM GM.2 | NCTM GM.3 TOP: Congruence transformations. KEY: congruence transformation 141. ANS: Sample: Given:  with ;  Prove:  Proof:  The slope of CA is  or . The slope of CB is  or . The slope of CD is  or. The slope of CF is  or . The slope of AB is  or . The slope of DF is  or .  because they are formed by segments of equal slopes.  because they are formed by segments of equal slopes.  because they are the same angle. Therefore, . PTS: 1 DIF: Average REF: Lesson 4-8 OBJ: 4-8.2 Solve multi-step problems. NAT: NCTM PS.1 | NCTM PS.2 | NCTM PS.3 TOP: Write coordinate proofs. KEY: Proofs | Coordinate Proofs 142. ANS: Sample: Given:  with coordinates , ,  Prove:  is isosceles Proof:   Since ,  and by definition the triangle is isosceles. PTS: 1 DIF: Basic REF: Lesson 4-8 OBJ: 4-8.2 Solve multi-step problems. 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PTS: 1 DIF: Average REF: Lesson 5-3 OBJ: 5-3.3 Solve multi-step problems. NAT: NCTM GM.1 | NCTM GM.1a | NCTM AL.2 | NCTM AL.2b | NCTM RP.1 TOP: Solve multi-step problems. KEY: Solve multi-step problems. 145. ANS:  If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side. PTS: 1 DIF: Advanced REF: Lesson 5-3 OBJ: 5-3.3 Solve multi-step problems. NAT: NCTM GM.1 | NCTM GM.1a | NCTM AL.2 | NCTM AL.2b | NCTM RP.1 TOP: Solve multi-step problems. KEY: Solve multi-step problems. 146. ANS: Sample: Given:  Prove:  is positive. Indirect Proof: Step 1: Assume a is not positive, or . Step 2: Case 1: Case 2:Step 3: Case 1 contradicts a being positive and Case 2 is a contradiction since no number is smaller than itself. Hence, the assumption must be false, and a is positive. PTS: 1 DIF: Average REF: Lesson 5-4 OBJ: 5-4.1 Use indirect proof with algebra. NAT: NCTM GM.1c | NCTM RP.1 TOP: Use indirect proof with algebra. KEY: Proofs | Indirect Proofs 147. ANS: Sample: Given: ,  Prove:  Indirect Proof: Step 1: Assume . Step 2:  (Angle Sum Theorem)  (Subtraction Property)  because .  (Linear Pair)  because . Step 3: This contradicts the given fact . Thus, . PTS: 1 DIF: Basic REF: Lesson 5-4 OBJ: 5-4.2 Use indirect proof with geometry. NAT: NCTM AL.2 | NCTM AL.2b | NCTM GM.1 TOP: Use indirect proof with geometry. KEY: Proofs | Indirect Proofs 148. ANS: Sample: Given: ; A is the midpoint of BF and CD. Prove:  Indirect Proof: Step 1: Assume  is not parallel to . Step 2: If  is not parallel to , then  is not congruent to . If  is not parallel to , then  is not congruent to . If those angles are not congruent, then the triangles cannot be congruent. However,  by the midpoint theorem, and  because they are vertical angles.  by SAS.  and  because corresponding parts of congruent triangles are congruent. Step 3: The assumption is false, so . PTS: 1 DIF: Average REF: Lesson 5-4 OBJ: 5-4.2 Use indirect proof with geometry. NAT: NCTM AL.2 | NCTM AL.2b | NCTM GM.1 TOP: Use indirect proof with geometry. KEY: Proofs | Indirect Proofs 149. ANS: Sample: Given:  with angle measures as shown Prove:  Indirect Proof: Step 1: Assume . Step 2: By angle-side relationships . Step 3: This contradicts the given angle measures, so the assumption must be false and . PTS: 1 DIF: Average REF: Lesson 5-4 OBJ: 5-4.2 Use indirect proof with geometry. NAT: NCTM AL.2 | NCTM AL.2b | NCTM GM.1 TOP: Use indirect proof with geometry. KEY: Proofs | Indirect Proofs 150. ANS: Yes, if you assume that Megan was the winner of the race, then she must have taken less time than the time taken by any of the participants in the race. But this contradicts the fact that Megan took more time than Sara to complete the race. Thus, the assumption that Megan was the winner of the race is false. Assume that the conclusion is false. 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