15. ANSWER: No, the polygons are not similar because the corresponding sides are not proportional.
Study Guide and Review Solve each proportion. 9. ANSWER: 49
16. ANSWER: Yes, the rectangles are similar because all of the corresponding angles are congruent and the corresponding sides are proportional in a 3:2 ratio.
10. ANSWER: –15
17. The two triangles in the figure below are similar. Find the value of x.
11. ANSWER: 10 or –10 ANSWER: 16.5
12. ANSWER: 4.5 13. The ratio of the lengths of the three sides of a triangle is 5:8:10. If its perimeter is 276 inches, find the length of the longest side of the triangle.
18. PHOTOS IF the dimensions of a photo are 2 inches by 3 inches and the dimensions of a poster are 8 inches by 12 inches, are the photo and poster similar? Explan. ANSWER: Yes; the ratios are the same.
ANSWER: 120 in.
Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning.
14. CARPENTRY A board that is 12 feet long must be cut into two pieces that have lengths in a ratio of 3 to 2. Find the lengths of the two pieces. ANSWER: 7.2 ft and 4.8 ft Determine whether each pair of figures is similar. If so, write the similarity statement and scale factor. If not, explain your reasoning.
19. ANSWER: Yes,
by the SAS
Thm.
15. ANSWER: No, the polygons are not similar because the corresponding sides are not proportional. 20. eSolutions Manual - Powered by Cognero
ANSWER: Yes,
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by the SSS
Thm.
he is standing 66 feet away from the tree, what is the height of the tree?
19. ANSWER: Study Guide and Review by the SAS Yes,
ANSWER: 34.2 ft
Thm.
Find x.
24. ANSWER: 9.6
20. ANSWER: Yes,
by the SSS
Thm.
25. ANSWER: 22.5 21. ANSWER: No, the triangles are not similar because not all corresponding angles are congruent.
26. STREETS Find the distance along Broadway between 37th St. and 36th St.
22. ANSWER: Yes,
ANSWER: 275 ft by the AA
Post.
23. TREES To estimate the height of a tree, Dave stands in the shadow of the tree so that his shadow and the tree’s shadow end at the same point. Dave is 6 feet 4 inches tall and his shadow is 15 feet long. If he is standing 66 feet away from the tree, what is the height of the tree?
Find the value of each variable.
27. ANSWER: 6
ANSWER: 34.2 ft Find x.
28. 24.
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ANSWER: 9.6
ANSWER: 19
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27.
31.
ANSWER: Study 6 Guide and Review
ANSWER: enlargement; 2 32. GRAPHIC DESIGN Jamie wants to use a photocopier to enlarge her design for the Honors Program at her school. She sets the copier to 250%. If the original drawing was 6 inches by 9 inches, find the dimensions of the enlargement.
28. ANSWER: 19 29. MAPS The scale given on a map of the state of Missouri indicates that 3 inches represents 50 miles. The cities of St. Louis, Springfield , and Kansas City form a triangle. If the measurements of the lengths of the sides of this triangle on the map are 15 inches, 10 inches, and 13 inches, find the perimeter of the actual triangle formed by these cities to the nearest mile. ANSWER: 633 mi Determine whether the dilation from A to B is an enlargement or a reduction. Then find the scale factor of the dilation.
ANSWER: 15 in. by 22.5 in. 33. BUILDING PLANS In a scale drawing of a school’s floor plan, 6 inches represents 100 feet. If the distance from one end of the main hallway to the other is 175 feet, find the corresponding length in the scale drawing. ANSWER: 10.5 in. 34. MODEL TRAINS A popular scale for model trains is the 1: 48 scale. If the actual train car had a length of 72 feet, find the corresponding length of the model in inches. ANSWER: 18 in. 35. MAPS A map of the eastern United States has a scale where 3 inches = 25 miles. If the distance on the map between Columbia, South Carolina, and Charlotte, North Carolina, is 11.5 inches what is the actual distance between the cities? ANSWER: 95.8 mi
30. ANSWER: reduction;
31. ANSWER: enlargement; 2 32. GRAPHIC DESIGN Jamie wants to use a photocopier to enlarge her design for the Honors Program at her school. She sets the copier to 250%. If the original drawing was 6 inches by 9 inches, find
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