1. GOAL 1 PROPORTIONS IN RIGHT TRIANGLES EXAMPLE 1 9.1 Similar Right Triangles THEOREM 9.1 If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other.

2. Extra Example 1 A roof has a cross section that is a right triangle. The diagram shows the approximate dimensions of this cross section. a. Identify the similar triangles in the diagram. b. Find the height h of the roof. 7.8 m12.3 m 14.6 m A B C D h

3. Checkpoint 6.8 in. 12.7 in. 14.4 in. S R U T h The diagram shows the approximate dimensions of a right triangle. a. Identify the similar triangles in the diagram. b. Find the height h of the triangle.

4. GOAL 2 USING A GEOMETRIC MEAN TO SOLVE PROBLEMS EXAMPLE 2 9.1 Similar Right Triangles Study the Geometric Mean Theorems on page 529 before going on!

5. Extra Example 2 Find the value of each variable. a.b. 610 x 5 8 y

6. Checkpoint Find the value of each variable. a. b. 1424 x 5 18 y

7. GOAL 2 USING THE PYTHAGOREAN THEOREM EXAMPLE 1 9.2 The Pythagorean Theorem If ΔABC is a right triangle, then c 2 = a 2 + b 2. a b c A B C

8. Extra Example 1 Find the length of the hypotenuse of the right triangle. Tell whether the side lengths form a Pythagorean triple. 7 24 x

9. Checkpoint Find the length of the hypotenuse of the right triangle. Tell whether the side lengths form a Pythagorean triple. x 2

10. Extra Example 2 12 x Find the length of the leg of the right triangle.

11. Checkpoint Find the length of the leg of the right triangle. 9 21 x

12. Extra Example 3 h 8 m 10 m Find the area of the triangle to the nearest tenth of a meter.

13. Extra Example 4 The two antennas shown in the diagram are supported by cables 100 feet in length. If the cables are attached to the antennas 50 feet from the ground, how far apart are the antennas?

14. Checkpoint Find the missing side of the triangle. Then find the area to the nearest tenth of a meter. 12 m 10.8 m