1. Objective The learner will solve problems using the Pythagorean Theorem

2. WHY? To find missing sides of right triangles & to calculate heights

3. Lesson 11 – 2 The Pythagorean Theorem Pages 584 - 590

4. Pythagorean Theorem Pythagoras Pythagorean Theorem Proof

5. In a right triangle, the side opposite the right angle is the hypotenuse. It is the longest side. Each of the sides forming the right angle is a leg. The Pythagorean Theorem describes the relationship of the lengths of the sides of a right triangle. hypotenuse legs

6. The Pythagorean Theorem In any right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. a² + b² = c² a b c

7. Example #1 What is the length of the hypotenuse of the triangle? a² + b² = c² 9² + 12² = c² 81 + 144 = c² 225 = c² √225 = √c² 15 = cThe hypotenuse is 15cm. 9 cm 12 cm c

8. Now you try: What is the length of the hypotenuse of a right triangle with legs of lengths 7 cm and 24 cm? You can also use the Pythagorean Theorem to find the length of a leg of a right triangle when you know the length of the hypotenuse and the other leg.

9. Example #2 A fire truck parks beside a building such that the base of the ladder is 16ft from the building. The fire truck extends its ladder 30ft to reach the top of the building. How high is the top of the ladder above the ground? See work on the board.

10. Now you try: Use the figure at the right. About how many miles is it from downtown to the harbor? Round to the nearest tenth of a mile. Harbor Downtown Highway 4mi 8mi b

11. Converse of Pythagorean Theorem If a triangle has sides of lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle with a hypotenuse of length c. You can use the converse of the Pythagorean Theorem to determine whether a triangle is a right triangle.

12. Example #3 Determine whether the given lengths are sides of a right triangle. a. 5in, 12in, and 13in a² + b² = c² 5² + 12² = 13² 25 + 144 = 169 169 = 169 So the triangle is a right triangle.

13. Now you try: A triangle has sides of lengths 10m, 24m, and 26m. Is the triangle a right triangle?

14. Open Book Page 584