Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Write a similarity statement relating the three triangles in each diagram.

See Problem 2.

Algebra Find the geometric mean of each pair of numbers.

12. 4 and 10
13. 3 and 48
14. 5 and 125
15. 7 and 9
16. 3 and 16
17. 4 and 49

See Problems 3 and 4.

Algebra Solve for x and y.

18. 
19. 
20. 
21. 

22. Architecture The architect's side view drawing of a saltbox-style house shows a post that supports the roof ridge. The support post is 10 ft tall. How far from the front of the house is the support post positioned?

    

B Apply

23. 1. The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments 2 cm and 8 cm long. Find the length of the altitude to the hypotenuse.
    2. Use a ruler to make an accurate drawing of the right triangle in part (a).
    3. Writing Describe how you drew the triangle in part (b).

Algebra Find the geometric mean of each pair of numbers.

24. 1 and 1000
25. 5 and 1.25
26. 8 square root of 8  and 2 square root of 2
27. 1 2 1 half  and 2
28. 28  and  7 square root of 28 , and , square root of 7
29. Reasoning A classmate says the following statement is true: The geometric mean of positive numbers a and b is a b . square root of eh b end root , .  Do you agree? Explain.
30. Think About a Plan The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments with lengths in the ratio 1 : 2. The length of the altitude is 8. How long is the hypotenuse?
    • How can you use the given ratio to help you draw a sketch of the triangle?
    • How can you use the given ratio to write expressions for the lengths of the segments of the hypotenuse?
    • Which corollary to Theorem 7-3 applies to this situation?

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