1. Chapter 7 Lesson 2 Objective: To Objective: To use the Pythagorean Theorem.

2. Theorem 7-4 Theorem 7-4 Pythagorean Theorem In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. a 2 + b 2 = c 2

3. A Pythagorean triple is a set of nonzero whole numbers a, b, and c that satisfy the equation a 2 + b 2 = c 2. Here are some common Pythagorean triples.Pythagorean triple 3,4,55,12,138,15,177,24,25

4. Example 1: Pythagorean Triples Find the length of the hypotenuse of ∆ ABC. Do the lengths of the sides of ∆ ABC form a Pythagorean triple? The lengths of the sides, 20, 21, and 29, form a Pythagorean triple.

5. Example 2: Pythagorean Triple A right triangle has a hypotenuse of length 25 and a leg of length 10. Find the length of the other leg. Do the lengths of the sides form a Pythagorean triple? Not a Pythagorean Triple

6. Example 3: Using Simplest Radical Form Find the value of x. Leave your answer in simplest radical form.

7. Example 4: Using Simplest Radical Form The hypotenuse of a right triangle has length 12. One leg has length 6. Find the length of the other leg. Leave the answer in simplest radical form.

8. The Parks Department rents paddle boats at docks near each entrance to the park. About how far is it to paddle from one dock to the other? It is about 430 m from one dock to the other. Example 5: Real-World Connection

9. Assignment Page 360 #1-17; 36-38