ࡱ> <>;y{` #bjbjFF 4d,,2@@@@000D N N N8DNlND8POPPPPPPfP$hFT0@@PPfPo^^^^@ PP0fP^^^(0fPDO Q N&08&L0'^5 AS^8DDD:MDDDDMDDD@@@@@@ A 139 EXAM THREE REVIEW PROBLEMS Note: This is NOT a practice exam. It is a collection of problems to help you review some of the material for the exam and to practice some kinds of problems. This collection is not necessarily exhaustive. We have covered material in this class that is not represented in this collection. You should expect some problems on the exam to look different from these problems. Be sure to also review your class notes, quizzes, homework assignments, and reading assignments. Some good problems from the book: Chapter 10 Test : 1, 2abcd, 3abcde, 6, 7 Chapter 11 Test : 3, 4, 10, 11, 12, 15, 16 Use a compass and protractor to construct the triangle STP with the following characteristics: ST = 1.25 inch, SP = 2 inches, and angle S = 40. What is the measure of angle T? Using a straightedge, ruler, compass, and protractor as necessary, show why it is impossible to construct a triangle with sides of length 1.5 inches, 2.75 inches, and 5 inches. Carefully construct triangle DEF with DE = 4 cm, EF = 6 cm, and angle DEF = 45. Measure and record on your sketch the length of the third side and the measure of the other two angles. Carefully construct triangle JPS with JP = 3 inches, angle SJP = 40, and angle JPS = 75. Measure and record on your sketch the length of the other two sides (rounded to the nearest eighth-inch). 5. Calculate the measurement conversion indicated. A. 3.4 miles = _______ feet C. 12 feet = ______ meters B. 17.5 yards = ______ miles D. 40 centimeters = ______ inches 6. Calculate the measurement conversion indicated. A. 50 square inches = _______ square feet B. 3.5 square miles = _______ square feet C. 250 square inches = ________ square centimeters D. 3 square meters = ________ square centimeters 7. Calculate the measurement conversion indicated. A. 40 pints = ______ gallons C. 8.5 pints = ______ cups B. 17 cups = ______ quarts D. 70 mph = ______ yards per minute 8. True-False. A statement should be marked false if it is never true or if it is not necessarily true. If a statement is only sometimes true, mark it as false. Explain briefly why any true statements are true, and explain briefly why any false statements are false or give a counter example. a. If two right triangles have congruent hypotenuses, then the triangles are congruent. b. If  EMBED Equation.DSMT36 , then  EMBED Equation.DSMT36 . c. In  EMBED Equation.DSMT36 , if  EMBED Equation.DSMT36 , then the triangles must be congruent. d. If the hypotenuse of one right triangle is twice the length of the hypotenuse of a second right triangle, then the triangles are similar. 9. Can you find a pair of congruent triangles in this figure? How do you know they are congruent? Potentially useful facts about the figure are given. [This is nastier than any problem Ill give on the exam, but its still good practice for you.]   EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4   10. Find the measure of  EMBED Equation.DSMT36 . 11. In this figure are any triangles similar? Why or why not? If you identify any similar triangles, write a similarity statement (e.g.,  EMBED Equation.DSMT36 ). 12. Find x and y in the figure below. 13. Find the distance across the river in the sketch below. (Pretend it is drawn to scale ()  14. Without measuring anything, what can you say about the scale factor for the projection illustrated here? Be as specific as you can without knowing or assuming any measurements.  15. In this figure are any triangles similar? Why or why not? If you identify any similar triangles, write a similarity statement (e.g.,  EMBED Equation.DSMT36 ).  16. Create an example of two quadrilaterals in which the sides of one are all one third the length of the sides of the other, yet the quadrilaterals are not similar. Label the lengths of the sides. 17. Wendy was talking about making similar rectangles. She said that by adding 2 units to the width and 3 units to the length, she ended up with similar rectangles. Two examples are shown here. What can you say about Wendys idea?  18. Are these triangles similar? Explain how you know.  19. A small town in Western Canada reports that its border is in the shape of a rectangle with dimensions 1.5 km ( 2.2 km. Find the area of this town in square miles and in acres. One acre is 43,560 square feet, and one mile is 1.61 km (or 0.621 mile is one km). 20. Find the area of the regular hexagon shown here. Explain completely how you found the area. Do not round your answer. (Hint: you may assume that the small triangles are isosceles triangles.)  21. Find the area and perimeter of the following region. All angles are right angles, and the curve is a semicircle. The sides marked as congruent measure one inch each. Show all calculations. Round answers to the nearest hundredth.  22. Find the area of the quadrilateral ABCD to the nearest hundredth of a square centimeter. (Hint: you can find the measure of diagonal AC.) Show your work, and explain with words your strategy. (This problem is harder than anything that will be on the exam.)  23. A regular hexagon is inscribed in a circle as shown below. Find each of the following areas: The area of the hexagon The area of the circle  24. Find the area of the shaded region:  25. A rectangular field is 64 m ( 25 m. Shawn wants to fence a square field that has the same area as the rectangular field. How long are the sides of Shawns field? 26. Find the exact area of this figure. Indicate how you found the area.  27. True or false: If one figure has less area than another figure, then the figure with the smaller area has the smaller perimeter. If this statement is true, explain why. If it is false, create a counterexample. 28. Two semicircular arcs, of radius 3 m and 5 m are centered on the diameter  EMBED Equation.DSMT36  of a large semicircle as shown.  What is the length of  EMBED Equation.DSMT36 ? Which route from A to B is shorter: along the large semicircle or along the two smaller semicircles? Show your work and how you came to your conclusion. 29. Find the perimeter to the nearest millimeter and the area to the nearest square millimeter of the triangle ABC below. Show and explain your work.      Math 139 Exam 3 Review Spring 2008 A 2 in. C B A B C D A 2 in. 2 in.  EMBED Equation.3 cm 48 mm 100 mm 6 cm 80 mm 5 m 3 m C B 18 32 26 44.2 54.4 1 unit of area 2 cm 2 cm 6 cm 2 cm 3 cm 30.6 3 + 3 = 6 2 + 2 = 4 3 2 5 5 + 3 = 8 3 + 2 = 5 3 12 8 4 9.6 6 8 E D C B A Image Figure O Z T W Y X The River 64 m 20 m 16 m y x 8 6 8 4 X W V A B D E F C U T E D C B A 9 in. 14 in. 4 in. 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