1. Lesson 9-5 Pages 460-464 The Pythagorean Theorem Lesson Check 9-4

2. What you will learn! 1.How to use the Pythagorean Theorem to find the length of a side of a right triangle. 2.Use the converse of the Pythagorean Theorem to determine whether a triangle is a right triangle.

3. LegsHypotenuse Pythagorean Theorem Solving a right triangle Converse

4. What you really need to know! Pythagorean Theorem If a triangle is a right triangle, then the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

5. What you really need to know! a c b a 2 + b 2 = c 2

6. Example: 3 5 4 3 2 + 4 2 = 5 2 9 + 16 = 25 25 = 25

8. Example 1: Find the length of the hypotenuse of the right triangle. 20ft c ft 21ft a 2 + b 2 = c 2 21 2 + 20 2 = c 2 441 + 400 = c 2 841 = c 2 29 = c

9. Example 2: Find the length of the leg of the right triangle. b mb m 11 m 8 m a 2 + b 2 = c 2 8 2 + b 2 = 11 2 64 + b 2 = 121 b 2 = 57 b ≈ 7.5 m

10. A building is 10 feet tall. A ladder is positioned against the building so that the base of the ladder is 3 feet from the building. How long is the ladder? A12.4B10.4C10.0D14.9 3 ft 10 ft Example 3:

11. Example 4: The measure of three sides of a triangle are given. Determine whether the triangle is a right triangle. 48 ft 60 ft 78 ft 48 2 + 60 2 ?=? 78 2 NO!

12. Example 4a: The measure of three sides of a triangle are given. Determine whether the triangle is a right triangle. 24 ft 70 ft 74 ft 24 2 + 70 2 ?=? 74 2 YES!

13. Page 462 Guided Practice #’s 3-9

15. Pages 460-462 with someone at home and study examples! Read:

16. Homework: Pages 463-464 #’s 10-36 even, 39, 40, and 44-52 Lesson Check 9-5

22. Page 746 Lesson 9-5

23. Lesson Check 9-5

24. Homework: Pages 463-464 #’s 10-21, 26-31, 34, 39, 40, 44-52 Lesson Check 9-5