Geometry - Loudoun County Public Schools



Geometry Name: ___________________

Review – CH 6Similar Triangles Block: ________ Date: ______

Write the algebraic ratio in simplest form. Find the geometric mean of the numbers.

1. [pic] 2. [pic] 3. 15 and 10 ________

Complete each statement.

4. [pic]. 5. [pic]

Find the value of x.

6. [pic] 7. [pic]

Two similar polygons are shown. Find the values of x, y, and z.

8. 9. 9.

Scale factor:___________ Scale factor:___________

x = _____, y = _______, z = _______ x = _____, y = _______, z = _________

Tell which postulate/theorem (AA, SSS, SAS) you would use to prove the two triangles are similar, and state the similarity.

10. 11.

Post/Thm:_______ Similarity:_____________ Post/Thm:_______ Similarity:_____________

Find the value of x.

12. 13. 14.

x = _______________ x = _______________ x = _______________

15. To estimate the height of a tree, Adele waited until the tops of the shadows

of the tree and a sign coincided. The sign is 2m high and the sign and the tree

have shadows of 6.4 m and 15.8 m.

Find the height of the tree rounded to the nearest tenth of a meter:

Complete.

16.[pic] 17.[pic]

18. [pic] 19. [pic]

20. [pic] 21. [pic]

Find the value of x.

22. 23. 24. 25.

x=______ x =______ x =______ x =______

26. 27. 28. 29.

x =______ x =______ x =______ x =______

Can the two triangles be proved similar? If so, state the similarity and tell which postulate or theorem (such as AA, SSS, SAS) you would use. If not, write no conclusion is possible.

30. 31.

32. 33.

34. Given: [pic]. 35.

Therefore,

A. [pic]

B.[pic]

C. [pic]

D. [pic]

36. 37.

38. Two ships leaving the same marina at the same time are 3.2 miles apart after sailing 2.5 hours. If they continue at the same rate and direction, how far apart will they be 2 hours later?

A. 2.56 miles B. 3.52 miles C. 5.76 miles D. 4.5 miles

39. Which triangle to the right is similar to [pic]?

40. Triangles ABC and DEF are similar and have measurements as shown. What is the measure of [pic]?

[pic]

41. Triangles ABC and EFG are similar with measurements as shown. What is the ratio [pic] ?

[pic]

42. Two vehicles, each moving from a point in a straight line away from each other at an angle, are 150 feet apart after 6 seconds. Both are moving at a constant rate, vehicle A at 50 feet per second and vehicle B at 40 feet per second.

How far apart are they after 15 seconds?

[pic]

43. In the figure, AE = 8, CE = 12, and BE = 5. What value for the measure of [pic] would make [pic] similar to [pic] ?

[pic]

44. Line segments AC and BD intersect at E, as shown in the figure. [pic], DE = 10,

BE = 15, and CE = 20. What is the measure of [pic]?

[pic]

45. (The triangles are similar) 46. (The triangles are similar)

x = _____ x = ______ y = _______

47. In the figure shown, PQ = 30, ST = 5 centimeters, and m[pic]PRQ = 48(.

48. A triangles angle measures are in the extended ratio of 1:3:5. Find the measures of the angles and then classify the triangle by its angles and sides.

49.

50. 3. A photo needs to be enlarged from an original length of 11 inches and a width of 8 inches to a size where the new width is 32 inches. What is the new length? What is the new scale factor?

51. Given a rectangle with a perimeter of 48 and a ration of length to width of 7:5. Find the dimensions and the area of the rectangle.

52. Suppose you want to be sure that a large rug is priced fairly. The price of a small rug (29 inches by 47 inches) is $79 and the price of the large rug (4 feet 10 inches by 7 feet 10 inches) is $299.

a. What are the areas of the two rugs? What is the ratio of the areas?

b. Compare the rug costs. Do you think the large rug is a good buy? Explain.

53. The ratio of the volumes of two similar solids is 64: 729. What is the area of the solids?

54. A dilation is made of a sphere using a scale factor of 3:1. By what factor does the volume of the sphere change?

-----------------------

Which proportion is true?

F. [pic]

G. [pic]

H. [pic]

J. [pic]

[pic] are parallel. Which of the following statements is true?

A. [pic]

B. [pic]

C. [pic]

D. [pic]

Given: [pic].

Which proportion is true?

F. [pic]

G. [pic]

H. [pic]

J. [pic]

6

n.3 [pic]

6

16

12

y

x + 8

x

x

8

12

10

Find [pic] _______

Write a similarity statement for the two triangles. ∆ STR ( ______

What is the scale factor? _______

[pic]

Karen wanted to measure the height of her school’s flagpole. She placed a mirror on the ground 46 ft. from the flagpole, and then walked backwards until she was able to see the top of the pole in the mirror. Her eyes were 5 feet above the ground and she was 11 feet from the mirror. Use similar triangles; find the height of the pole.

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