2. Lesson Menu Main Idea and New Vocabulary Key Concept:Pythagorean Theorem Example 1:Find a Missing Length Example 2:Find a Missing Length Key Concept:Converse of Pythagorean Theorem Example 3:Identify a Right Triangle

3. Main Idea/Vocabulary Use the Pythagorean Theorem. legs hypotenuse Pythagorean Theorem converse

4. Key Concept

5. Example 1 Find a Missing Length Write an equation you could use to find the length of the missing side of the right triangle. Then find the missing length. Round to the nearest tenth if necessary. a 2 + b 2 = c 2 Pythagorean Theorem 12 2 + 16 2 = c 2 Replace a with 12 and b with 16. 144 + 256 = c 2 Evaluate 12 2 and 16 2. 400 = c 2 Add 144 and 256.

6. Example 1 Find a Missing Length Answer: So, the hypotenuse is 20 inches long. Definition of square root c = 20 or –20Simplify. The equation has two solutions, 20 and –20. However, the length of a side must be positive.

7. Example 1 CYP A.18 + 9 = c; c = 27 cm B.18 2 + 9 2 = c 2 ; c = 20.1 cm C.18 2 – 9 2 = c; c = 243 cm D.18 2 – 9 2 = c 2 ; c = 15.6 cm Write an equation you could use to find the length of the missing side of the right triangle. Then find the missing length. Round to the nearest tenth if necessary.

8. Example 2 Write an equation you could use to find the length of the missing side of the right triangle. Then find the missing length. Round to the nearest tenth if necessary. Find a Missing Length a 2 + b 2 = c 2 Pythagorean Theorem a 2 + 28 2 = 33 2 Replace b with 28 and c with 33. a 2 + 784 = 1,089 Evaluate 28 2 and 33 2.

9. Example 2 Find a Missing Length a 2 + 784 – 784 = 1,089 – 784 Subtract 784 from each side. a 2 = 305 Simplify. Definition of square root a  17.5 or –17.5 Use a calculator. Answer: The length of side a is about 17.5 centimeters.

10. Example 2 CYP A.12 + b 2 = 37; 5 ft B.12 + b = 37; 25 ft C.12 + b 2 = 37 2 ; 36.8 ft D.12 2 + b 2 = 37 2 ; 35 ft Write an equation you could use to find the length of the missing side of the right triangle. Then find the missing length. Round to the nearest tenth if necessary.

11. Key Concept 2

12. Example 3 Identify a Right Triangle The measures of three sides of a triangle are 24 inches, 7 inches, and 25 inches. Determine whether the triangle is a right triangle. a 2 + b 2 = c 2 Pythagorean Theorem 24 2 + 7 2 = 25 2 a = 24, b = 7, c = 25 576 + 49= 625 Evaluate 24 2, 7 2, and 25 2. 625= 625 Simplify. Answer: The triangle is a right triangle.

13. Example 3 CYP A.yes B.no The measures of three sides of a triangle are 10 centimeters, 12 centimeters, and 14 centimeters. Determine whether the triangle is a right triangle.