The document discusses the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs. It provides examples of using the theorem to find missing sides of right triangles and the area of a triangle when two sides and a height are known.

1. The Pythagorean Theorem - 9.2 Objectives: Prove the Pythagorean Theorem Use Pythagorean to solve problems

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

3. Proving Pythagorean Look at page 535

4. Using Pythagorean A Pythagorean triple is a set of 3 positive integers a, b, and c that satisfy the equation c 2 = a 2 + b 2 3, 4, and 5 are an example.

5. Using Pythagorean If the legs are 5 and 12, what is the hypotenuse? 5*5 + 12*12 = 25 + 144 = 169 √ 169 = 13 5, 12, and 13 are Pythagorean triples.

6. Find the length of the hypotenuse: x 2 = 5 2 + 12 2 x = √25 + 144 x = 13 x 5 12

7. Find the length of the leg: 14 2 = 7 2 + x 2 196 = 49 + x 2 147 = x 2 x = 7√3 14 7 x

8. Find the area of a triangle: Find the height: 7 2 = 5 2 + h 2 49 = 25 + h 2 24 = h 2 h = √24 7 m 7 m 10 m

9. Find the area of a triangle: Now find the Area: A = 1/2 b*h A = 1/2 * 10 * √24 A = 24.5 m 2 7 m 7 m 10 m

10. Now do Example 4, p. 537

11. Pythagorean video

12. Homework Do worksheets.