1. Then/Now You have already found missing measures of similar triangles. (Lesson 6–7) Use the Pythagorean Theorem to find the length of a side of a right triangle. Use the converse of the Pythagorean Theorem to determine whether a triangle is a right triangle.

2. Vocabulary legs hypotenuse Pythagorean Theorem solving a right triangle converse

3. Concept

4. Example 1 Find the Hypotenuse Length Find the length of the hypotenuse of the right triangle.

5. A.A B.B C.C D.D Example 1 Find the length of the hypotenuse of the right triangle.

6. Example 2 A ladder positioned against a 10-foot building reaches its top. Its base is 3 feet from the building. About how long is the ladder in feet? Round to the nearest tenth.

7. A.A B.B C.C D.D Example 2 An 18-foot ladder is placed against a building which is 14 feet tall. About how far is the base of the ladder from the building?

8. Example 3 Solve a Right Triangle LANDSCAPING A diagonal path through a rectangular garden is 32 feet long. The length of the garden is 24 feet. About how many feet wide is the garden?

9. A.A B.B C.C D.D Example 3 LANDSCAPING A diagonal path through a rectangular garden is 40 feet long. The length of the garden is 30 feet long. About how many feet wide is the garden?

10. Example 4 A Identify a Right Triangle A. The measures of three sides of a triangle are given. Determine whether the triangle is a right triangle. 48 ft, 60 ft, 78 ft

11. Example 4 Identify a Right Triangle B. The measures of three sides of a triangle are given. Determine whether the triangle is a right triangle. 24 cm, 70 cm, 74 cm

12. A.A B.B Example 4 CYP A A. The measures of three sides of a triangle are given. Determine whether the triangle is a right triangle. 42 in., 61 in., 84 in.

13. A.A B.B Example 4 CYP B B. The measures of three sides of a triangle are given. Determine whether the triangle is a right triangle. 16 m, 30 m, 34 m