Study Guide and Review Solve each proportion. 9. SOLUTION:
Cross multiply.
Solve for x.
10. SOLUTION:
Cross multiply.
Solve for x.
11. SOLUTION:
Cross multiply.
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Study Guide and Review
11. SOLUTION:
Cross multiply.
Solve for x.
12. SOLUTION:
Cross multiply.
Solve for x.
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. SOLUTION: Just as the ratio
or 5:8 is equivalent to
or 5x:8x , the extended ratio can be written as 5x:8x:10x.
The perimeter is 276 inches, so the sum of the lengths of the sides is 276. Solve for x. .
So the measures of the three sides are 5(12) or 60, 8(12) or 96, and 10(12) or 120. Thus the length of the longest side is 120 inches. Determine whether each pair eSolutions Manual - Powered by Cognero not, explain your reasoning.
of figures is similar. If so, write the similarity statement and scale factor.Page If 2
SoGuide the measures of the three sides are 5(12) or 60, 8(12) or 96, and 10(12) or 120. Thus the length of the longest side Study and Review is 120 inches. Determine whether each pair of figures is similar. If so, write the similarity statement and scale factor. If not, explain your reasoning.
15. SOLUTION: Step 1: Compare corresponding angles:
All corresponding angles are congruent.
Step 2: Compare corresponding sides:
Since
, the figures are not similar.
No, the polygons are not similar because the corresponding sides are not proportional.
16. SOLUTION: Step 1: Compare corresponding angles:
Since all of the angles in the polygons are right angles, they are all congruent to each other. Therefore, corresponding angles are congruent. Step 2: Compare corresponding sides:
Since
, the corresponding sides of the polygons have the same scale factor, which is .
Yes, the rectangles are similar because all of the corresponding angles are congruent and the corresponding sides are proportional in a 3:2 ratio.
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17. The two triangles in the figure below are similar. Find the value of x.
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Since
, the figures are not similar.
Study Guide and Review No, the polygons are not similar because the corresponding sides are not proportional.
16. SOLUTION: Step 1: Compare corresponding angles:
Since all of the angles in the polygons are right angles, they are all congruent to each other. Therefore, corresponding angles are congruent. Step 2: Compare corresponding sides:
Since
, the corresponding sides of the polygons have the same scale factor, which is .
Yes, the rectangles are similar because all of the corresponding angles are congruent and the corresponding sides are proportional in a 3:2 ratio. 17. The two triangles in the figure below are similar. Find the value of x.
SOLUTION: If two triangles are similar, then their corresponding sides are proportional.
Form a proportion and solve for x.
Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning.
19. SOLUTION: By the Reflexive Property,
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.
Study Guide and Review Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning.
19. SOLUTION: By the Reflexive Property,
.
So,
by SAS Similarity.
20. SOLUTION:
.
So,
by SSS Similarity.
21. SOLUTION:
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No, the triangles are not similar because not all corresponding angles are congruent.
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.
Guide and Review Study So, by SSS Similarity.
21. SOLUTION:
No, the triangles are not similar because not all corresponding angles are congruent.
22. SOLUTION: Since Yes,
, then congruent alternate interior angles are formed. Therefore,
.
by the AA Similarity 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? SOLUTION: Make a sketch of the situation. 4 feet 6 inches is equivalent to 4.5 feet.
In shadow problems, you can assume that the angles formed by the Sun’s rays with any two objects are congruent and that the two objects form the sides of two right triangles.
Since two pairs of angles are congruent, the right triangles are similar by the AA Similarity Postulate. So, the following proportion can be written.
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Convert all measures to inches:
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SOLUTION: Since , then congruent alternate interior angles are formed. Therefore, Guide and Review Study Yes, by the AA Similarity 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? SOLUTION: Make a sketch of the situation. 4 feet 6 inches is equivalent to 4.5 feet.
In shadow problems, you can assume that the angles formed by the Sun’s rays with any two objects are congruent and that the two objects form the sides of two right triangles.
Since two pairs of angles are congruent, the right triangles are similar by the AA Similarity Postulate. So, the following proportion can be written.
Convert all measures to inches: 81 ft = 972 inches
6 feet 4 inches = 76 inches
15 feet = 180 inches.
Let x be the tree’s height. Substitute and solve for x:
So, the tree is 410.4 inches or 34.2 feet tall. Find x.
24. SOLUTION: eSolutions Manual - Powered by Cognero
Solve for x.
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Guide and Review Study So, the tree is 410.4 inches or 34.2 feet tall. Find x.
24. SOLUTION:
Solve for x.
25. SOLUTION:
Solve for x.
26. STREETS Find the distance along Broadway between 37th St. and 36th St.
SOLUTION: Assuming that 38th street, 37th street and 36th street are parallel to each other, we can set up a proportion using the triangle proportionality Theorem:
.
Solve for x.
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Solve for x. Study Guide and Review 26. STREETS Find the distance along Broadway between 37th St. and 36th St.
SOLUTION: Assuming that 38th street, 37th street and 36th street are parallel to each other, we can set up a proportion using the triangle proportionality Theorem:
.
Solve for x.
The distance between 37th St. and 36th St is 220 ft. Find the value of each variable.
27. SOLUTION: An angle bisector in a triangle separates the opposite side into two segments that are proportional to the lengths of the other two sides.
28. SOLUTION: An angle bisector in a triangle separates the opposite side into two segments that are proportional to the lengths of eSolutions Manualtwo - Powered Page 9 the other sides.by Cognero
Study Guide and Review
28. SOLUTION: An angle bisector in a triangle separates the opposite side into two segments that are proportional to the lengths of the other two sides.
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