15 x. x x. x 2. x y. c d. Honors Geometry Chapter 8 Review. Find the value of x and/or y in each proportion. x Solve for x. 6. Solve for x.

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1 Honors Geometry hapter 8 Review Name Find the value of x and/or y in each proportion y y 14 x 1 x 5 x 3 x 2 3. x x 4. x y 2x y y x Solve for x. x x 1 x 4 x 8 6. Solve for x. x x 2 6 x x 5 Find the specified value for each problem. 7. Name the Means and the Extremes of the proportion: a b c d 8. Find the fourth proportional to 4, 6, and Find the mean proportionals between 5 and 20. Means: Extremes:

2 10. Find the geometric means between 3 and If 9x 4y, find the ratio of x to y. 12. If r a 3x 2b, what is the value of x in terms of a, b, and r? 13. If 7 9, find the ratio of y to x. x 4y 2x y 14. Given: Δ~ΔEF, with lengths as shown. Find: F and EF T ~ OG 15. Given: m 70 m T ( x 10) m 2x Find: x and m T 16. If a school s 54-foot flagpole casts a 63-foot shadow, how long will the shadow be for a 6-foot tall girl standing near the flagpole? 17. E ~ MR OP Find: RP and OP 4 E 3 6 x y x = y = RP = OP =

3 19. ΔPQR~ΔEF. The sides of ΔEF are 2, 3, and 4. One side of ΔPQR is 5. Find the maximum perimeter possible for ΔPQR. 20. Michael is 3 ft from a lamppost that is 12 ft high. He is 5.5 ft tall. How long is Michael s shadow? 21. In the diagram, if ΔO is a dilation of ΔO, then find the coordinates for point. 22. RSQ ~ Find the value of x. P 4 S 5 R x Q 23. Find the value of x and y. 24. ~ PQR x = y = x = y = x = x =

4 x = 29. E a = b = c = 30. a) Find the scale factor of MNL to QRP. b) Find the perimeter of QRP. x = Use the picture to find each segment length. Match your answer to choices,,, or at the right. 31. GF F E FE Find the specified value for each problem. 35. Pentagon E is similar to pentagon E. The pentagons respective perimeters are 24 and 30. If =6, find. 36. radio antenna that is 100 m tall casts an 80-m shadow. t the same time, a nearby telephone pole casts a 16-m shadow. Find the height of the telephone pole.

5 37. Given: bisects = 8, = 6, = 5 Find: 38. Find the value of x. 8 x Given: EF // GO// HM // JK FG = 2, GH = 8, HJ = 5, EM = 6 Find: EO and EK 40. If PQ = 30, find the coordinates of Q in the diagram. P F G H J 24 E O M K Q R ( 3, 0) S (5, 0) 41. One side of a triangle is 4 cm shorter than a second side. The ray bisecting the angle formed by these sides divides the opposite side into 4-cm and 6-cm segments. Find the perimeter of the triangle. 42. Given: PT // RS NP = 5x 21, PR = 5, NT = x, TS = 8 Find: NR + NS N P T R S

6 First Second Third Fourth 43. The diagram shows a part of the town of Oola, La. First, Second, Third, and Fourth streets are each perpendicular to Elmwood venue. If the total frontage on Sandwick ourt is 400m, find the length of each block of Sandwick ourt. Sandwick ourt QS // PT 44. Given: TQ bisects RTP Find: QP, RS, and QS R Q 6 S 21 80m 100m 140m Elmwood venue P 28 T 45. Given: Δ~ ΔEF, with lengths as shown in the diagram Find: F= EF= 46. In the diagram, if ΔOKM is a dilation of ΔOHJ, then find the coordinates for point K. Scale factor= Ratio of perimeters: Ratio of corresponding angles: K H(0, 3) 10 E F O J (4, 0) M (12, 0)

7 47. Find the values of x and y. 48. Given: EM = 6, MI = 12, and EY = 10 Fill in the blank and then find YL. ΔEMY~ Δ E 9 12 M 4 6 x Y y I L 49. If the perimeter of Δ is 55, find. 50. You take a picture of a painting at an art gallery. The painting is above eye level, and you frame the painting so the top and bottom match up with the top and bottom of your view finder. Your camera s auto-focus feature focuses at the height of the angle bisector shown in the diagram. How far from the bottom of the painting is the focus? If KP = 15, FG = 2, GN = 3, and NJ = 4, find KM, MO, and OP. 52. Find x in trapezoid x 20

8 53. 5-foot tall girl is standing 13 feet from a 15-foot tall lamppost. How long is her shadow? (You will have to draw your own picture on the quiz!) x etermine whether each statement is true lways, Sometimes, or Never. 54. Two isosceles triangles are similar if a base angle of one is congruent to a base angle of the other. 55. Two isosceles triangles are similar if the vertex angle of one is congruent to the vertex angle of the other. 56. n equilateral triangle is similar to a scalene triangle. 57. If two sides of one triangle are proportional to two sides of another triangle, the triangles are similar. 58. If a line intersects a side of a triangle at one of its trisection points and is parallel to a second side, then it intersects the third side at one of its trisection points. 59. Two right triangles are similar if the legs of one are proportional to the legs of the other. 60. If the ratio of the measures of a pair of corresponding sides of two polygons is 3:4, then the ratio of the polygons perimeters is 5:6. etermine whether each statement is true or false. 61. If two triangles are similar, then they are congruent. 62. If two triangles are congruent, then they are similar. 63. n obtuse triangle is similar to an acute triangle. 64. Two right triangles are similar. 65. Two equilateral triangles are similar. 66. Two regular hexagons are similar. 67. Two rectangles are similar.

9 omplete the following proofs. 68. Given: 1 2 Prove: F E E 2 F 1 E TVPX trapezoid 69. Given: VP YP Prove: TY XY VP VY T V Y X P

10 RXZ parallelogram 70. Given: 3 4 Prove: R YZ RW Z Z 3 4 Y R W X