Name:



GEOMETRYName: ___________________________2015 Midterm Review Period: ____ Date: ___________To be prepared for your midterm, you will need to PRACTICE PROBLEMS and STUDY TERMS from the following chapters. Use this guide to help you practice.Chapter 1 (1.1 – 1.4):Points Lines and PlanesSegments and CongruenceMidpoint and Distance FormulasMeasure and Classify AnglesDescribe Angle Pair RelationshipsChapter 2:Conditional Statements (Converse, Inverse, Contrapositive, Biconditional)Postulates and DiagramsReasoning Properties from AlgebraProving Geometric StatementsChapter 3 (3.1 – 3.6):Parallel Lines and Angle Relationships (Corresponding, Consecutive, Alternate Interior/Exterior)Perpendicular LinesFind and Use Slopes of LinesWrite and Graph Equations of LinesChapter 4 (4.1 – 4.7):Triangle Classification (Acute, Obtuse, Right, Equiangular, Equilateral, Scalene, Isosceles)Triangle Sum PropertiesTriangle Congruence (SSS, SAS, AAS, ASA, HL)Isosceles and Equilateral Triangle PropertiesChapter 5 (5.5 – 5.6):Inequalities in a TriangleRelationships Between Side Lengths and Angle MeasuresInequalities in Two Triangles (Hinge Theorem)Chapter 6:Ratios, Proportions, Geometric MeanProve Triangles are Similar (AA, SSS, SAS)Use Proportionality TheoremsGeometryName: ___________________________Midterm Review Period: ____ Date: ___________1) Ray PR is shown in which sketch? a) b) c) d)2) If RS = 32.2 and QS = 62.8, find QR.3) Use the Segment Addition Postulate to solve for p.FE = 4p + 20EG = 5p + 16FG = 45a) p = 1b) p = 4c) p = 5d) p = 64) Find the distance between A(6, 0) and B(4, 4).a) 116b)c) d) 205) Find the midpoint of A(6, 0) and B(4, 4).6) M is the midpoint of segment AB. Given the coordinates of A(2, 4) and M(4, 6), find the coordinates of B.7) Which of the following angles measures 125? a) b) c)d) 8) If mJOL = 50 and mKOL = 27, then what is the measure of JOK?a) 25b) 23c) 28d) 209) Given that mGED=60, mGEF=2x + 7 and mDEF=7x – 1, find mGEF and mDEF.10) In the figure below, mAED = 128. Which of the following statements is false?a) mBEC = 128b) AEB and DEC are congruentc) BEC and CED are vertical anglesd) mAEB = 52 11) 1 and 2 are ______.a) a linear pairb) complementary anglesc) supplementary anglesd) vertical angles12) Find the measure of 1. 142a) 42b) 48c) 58d) 13813) Solve for x.14) Solve for x.15) Name an angle that is adjacent to BOCa) DOEb) AOEc) DOBd) BOA16) Using the diagram, name an angle that is complementary to COD.a) AOE b) BOC c) DOE d) AOC 17) Rewrite the statement in if-then form: Vertical angles are congruent.18) What is the converse of the statement, “If it rains then I carry my umbrella.”?a) “If it does not rain, then I do not carry my umbrella.”b) “If I do not carry my umbrella, then it does not rain.”c) “If I do not carry my umbrella, then I will get wet.”d) “If I carry my umbrella, then it rains.”19) “If I get a chance then I will succeed.” In this conditional statement, the underlined portion is called the __________________________.20) What is the inverse of the statement, “If two lines are parallel, then they do not intersect.”?a) “If two lines are not parallel then they intersect.’b) “If two lines intersect then they are not parallel.”c) “If two lines do not intersect then they may be skew.”d) “If two lines do not intersect then they are not parallel.”21) Which of the following statements is false?a) Three non-collinear points determine a plane.b) Any three points are collinear.c) A line contains at least two points.d) Through any two distinct points there exists exactly one line.22) Rewrite the biconditional statement as a conditional statement and its converse.Biconditional: “I am lactose intolerant if and only if I am allergic to milk products”Conditional:Converse:23) Write the converse of the conditional statement and decide if the statement can be written as a biconditional.If I got a speeding ticket, then I was exceeding the speed limit.Converse:Biconditional?24) State a counterexample to the following statement:“If x2 = 25, then x = 5.”a) x = 5b) x = 5c) x2 = 25d) x 2 = 10025) The figure at right represents which of the following statements?a) two perpendicular raysb) two perpendicular linesc) a straight angled) AB = AC26) Define each of the following terms.- Deductive reasoning- Inductive reasoning27) Provide an example of each of the following:- Law of Syllogism- Law of Detachment28) In the cube shown at right, are called _____ a) parallel linesb) perpendicular linesc) intersecting linesd) skew lines 29) In the figure shown, 1 and 2 are ____a) same-side interior anglesb) corresponding anglesc) alternate interior anglesd) alternate exterior angles30) In the figure, 6 and 3 are _____A) corresponding anglesB) alternate interior anglesC) alternate exterior anglesD) consecutive interior angles31) In the figure above, 6 and 2 are ____________________________________ angles.32) Find m1, given that a) 11 b) 79 c) 91 d) 10133) Complete the following 2-column proof:Given: & GivenGivenProve: 34) Write a proof of the following:Given: &Prove: Given35) Write a proof of the following:Given: &Prove: Given36) Complete the following statements:If , then the triangle is a _____________ triangle. If , then the triangle is an _____________ triangle.If , then the triangle is an _____________ triangle.37) In the figure, and r is a transversal. Which of the following is not necessarily true?a) 2 6b) 8 2c) 7 4d) 5 338) In the figure shown, , and mABC = 108. Which of the following statements is false?a) mDEF = 72b) ABH and AEG are alternate exterior anglesc) HBF and AED are alternate interior anglesd) mGEF = 10839) Find the slope of the line passing through the points (1, 6) and (6, 5).40) A line parallel to is: a) b) c) d) 41) Which describes the relationship between the lines with equations and a) parallel b) same line c) perpendicular d) neither parallel nor perpendicular42) Classify NOP.a) Equilateral b) Isosceles c) Scalene d) none of these43) Name an obtuse triangle in the diagram at right.44) Find the value of x.a) 80 b) 100 c) 160 d) 17045) Solve for x.46) Which figures appear to be congruent?a) 3 and 4b) 1, 2, and 4c) 2 and 5d) 1 and 447) If ABC XYZ, then ______.48) If JKL STU, JK = 10 feet, mK = 59, and mU = 21, which of the following is false?a) JL = SU b) KL = TU c) mS = 100 d) K S49) In the diagram, B E and C F. Find the value of x.50) What must be true for ABC EDC by SAS?a) B Db) c) d) A E51) Which of the following statements must be true, if AD BC and AB = AC?a) ABD ACD by SSSb) ABD ACD by SASc) ABD ACD by HLd) There are no congruent triangles52) Refer to the figure at right. ABC _____a) EDCb) EDAc) ACEd) CDEABCDE53) Using just the information shown in the diagram, which postulate or theorem can be used to prove that ABC EDC?54) What is the measure of each base angle of an isosceles triangle if its vertex angle measures 32 and its 2 congruent sides measure 17 inches?55) In ABC, if and mA = 39, then mC = ______.a) 39b) 51c) 102d) 14156) Find the values of x and y.a) x = 70 and y = 50b) x = 40 and y = 110c) x = 40 and y = 70d) x = 70 and y = 11057) Identify the longest side of the triangle.58) Arrange the angles of the triangle in order, from largest to smallest.a) P, Q, Rb) P, R, Qc) Q, R, Pd) Q, P, R59) The longest side in the figure is _______a)b) c) d) 60) Two sides of a triangle have lengths 12 and 27. The length of the third side must be greater than _____ and less then _____.a) 14, 40b) 15, 39c) 11, 28d) 12, 2761) Which side lengths allow you to construct a triangle?a) 7, 2, and 2 b) 2, 3, and 8 c) 1, 4, and 9 d) 6, 8, and 1062) Which Geometric concept do you think you could use later in life? Give an example.A63) In the figure shown, mAED = 110. Which statement is false?DCEa) mAEB = 80Bb) AEB and DEC are vertical anglesc) BEC and CED are adjacent anglesd) mBEC = 110 1a64) If line a is parallel to line b, what is m1?40b65) Lines and intersect at P. is perpendicular to and mAPD = 170. What is the measure of DPB?a) 10b) 20c) 30d) 4066) A ladder is leaning against a house at an angle of 38, as shown in the diagram. What is the measure of the angle x, that the ladder makes with the ground?124a67) Line a is parallel to line b if:3a) m4 = m2b) m3 = m565bc) m4 = m5d) m3 = m27868) ABC is a right triangle with right angle at C. Which are the possible measures of A and B?a) 48 and 50b) 38 and 32c) 52 and 38d) 52 and 12869) Which conclusion follows logically from the true statements?“If negotiations fail, then the baseball strike will not end.”“If the baseball strike does not end, then the World Series will not be played.” a) If the baseball strike ends, the World Series will be played. b) If negotiations do not fail, the baseball strike will end. c) If negotiations fail, the World Series will not be played. d) If negotiations fail, the World Series will be played.70) Given that and , which could be used to prove that DCA CDB?a) SSSb) SASc) ASAd) AAS71) On the shores of a river, surveyors marked locations A, B, and C. mACB = 70 and mABC = 65. Which lists the distances between these locations in order, least to greatest?BCA72) The figure has angle measures as shown. What is mBCD?373) What is m3?150a) 65b) 7565c) 85d) 9074) Which of the following could be the lengths of the sides of ABC?a) AB = 12, BC = 15, AC = 2b) AB = 9, BC = 15, CA = 4c) AB = 150, BC = 100, CA = 50d) AB = 10, BC = 8, AC = 1275) To find the contrapositive of a conditional statement you should:a) Find the inverse of the converse of the original statement.b) Find the converse of the inverse of the original statement.c) Negate the hypothesis and conclusion of the converse of the original statement.d) All of the above.76) Three lookout towers are located at points A, B, and C on a section of the national forest shown in the diagram. Which of the following is true concerning ABC formed by the towers?Ca) mA is greatestb) mC is greatest4123 km5385 kmc) mA is least4472 kmBAd) mC is least77) What value of x will make lines l and m parallel?4x - 902x + 30DC78) In the figure, mCAD is twice mCAB.B What is mCAB?a) 120Ab) 60c) 45d) 3079) Triangle XYZ is a right triangle with the right angle at Z. Which are possible measures for angle X and angle Y?a) 40 and 42b) 44 and 46c) 48 and 50d) 52 and 5480) Explain the difference between similar triangles and congruent triangles. Be specific.Questions 81-94: True/False. 81) It is possible to have a triangle with side lengths 7, 7, and 9.a) Trueb) False82) Corresponding parts of congruent triangles are equal in measure. a) Trueb) False83) Coplanar points are collinear. a) Trueb) False84) Collinear points are coplanar. a) Trueb) False85) SSA is a method to prove triangle congruency. a) Trueb) False86) When two planes intersect, they form a line. a) Trueb) False87) Equilateral triangles are equiangular. a) Trueb) False88) Skew lines are coplanar. a) Trueb) False89) If two lines are parallel, they have the same slope. a) Trueb) False90) A right triangle can have up to two right angles. a) Trueb) False91) In a right triangle, the hypotenuse is adjacent to the right angle. a) Trueb) False92) The slope of a horizontal line is zero. a) Trueb) False93) The AAA method is used to prove that triangles are congruent. a) Trueb) False94) A scalene triangle never has congruent sides. a) Trueb) FalseComplete the following sentences with always, sometimes, or never.95) An isosceles triangle is _____________________ a right triangle.96) An obtuse triangle is _____________________ a right triangle.97) A right triangle is _____________________ an equilateral triangle.98) A right triangle is _____________________an isosceles triangle.99) Simplify the following ratio as much as possible: a) b) c) d) 100) Solve the proportion: 101) In the diagram ABC ~ XYZ. Find YZ.a) 9/2 b) 2 c) 5 d) 8102) Let p represent “Line AB and line BC are perpendicular” and let q represent “ABC is a right angle”. Which represents the contrapositive of “If line AB and line BC are perpendicular, then ABC is a right angle”?a) q → pb) q → ~pc) ~q → pd) ~q → ~p103) Are the two triangles in this diagram similar? If so, give the similarity statement.a) Yes, ABC ~ CDEb) Yes, ABD ~ EDCc) Yes, ABD ~ ECDd) No, the triangles are not similar.104) In the diagram shown on the right, what is the length of ?a) 4 b) 3/2 c) 8/3 d) 16105) If two sides of a triangle have lengths 7 and 11, which is a possible length for the third side of the triangle?18542106) The coordinates of the midpoint of line segment CD are (4, -5) and the coordinates of C are (8, -8). What are the coordinates of D?107) If two triangles have one pair of congruent angles and if the lengths of the corresponding adjacent sides are proportional, then the triangles are:a) equalb) congruentc) similard) obtuse108) The ratio of the volumes of two similar rectangular prisms is 64:125. What is the ratio of their surface areas? ................
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