1. Exploring

2. Pythagorean Theorem For any right triangle, the area of the square on the hypotenuse is equal to the sum of the areas of the squares on the legs. Note: The hypotenuse is always the longest side of a right triangle. We can verify if a triangle is a right triangle by checking if this equation is satisfied.

3. The Pythagorean Theorem Example 1: Determine whether a triangle with side lengths 5 cm, 9 cm, and 6 cm is a right triangle. c = longest side = 9 cma and b = legs = 5 cm and 6 cm a 2 + b 2 c 2 = 5 2 + 6 2 = 9 2 = 25 + 36= 81 = 61= 81 Since 61 ≠ 81, the Pythagorean theorem is not satisfied, so the triangle is not a right triangle. If it were a right triangle, then a 2 + b 2 would give the same number as c 2.

4. The Pythagorean Theorem Example 2: Determine whether a triangle with side lengths 11, 61, 60 is a right triangle. c = longest side = 61 cma and b = legs = 11 cm and 60 cm a 2 + b 2 c 2 = 11 2 + 60 2 = 61 2 = 121 + 3600= 3721= 3721 Since 3721 = 3721, the Pythagorean theorem is satisfied, so the triangle is a right triangle. A set of three whole numbers that satisfies the Pythagorean Theorem is called a Pythagorean triple.

5. Classwork Page: 43-45 #3,5,6ab,8-10,12-14