1. How can you prove the Pythagorean Theorem by using the diagram below?

2. In this lesson you will learn how to prove the Pythagorean Theorem by using squares and triangles.

3. Let’s Review Hypotenuse Leg Leg

4. 90 0 120 0 60 0 75 0 45 0

5. Let’s Review A Common Mistake Which side is the hypotenuse? 9 in 15 in 12 in

6. Let’s Review Core Lesson 9 cm 2 16 cm 2 25 cm 2 3 2 + 4 2 = 5 2 9 + 16 = 25 25 = 25 3 cm 4 cm 6 6 6 6 1 5 cm

7. Let’s Review Core Lesson Pythagorean Theorem a 2 + b 2 = c 2 a c leghypotenuse bleg leg 2 + leg 2 = hypotenuse 2

8. Let’s Review Core Lesson leg 2 + leg 2 = hypotenuse 2 3 2 + 8 2 = 10 2 9 + 64 = 100 8 cm 10 cm 3 cm

9. Let’s Review Core Lesson leg 2 + leg 2 = hypotenuse 2 6 2 + 8 2 = 12 2 36 + 64 = 144 8 cm 12 cm 6 cm

10. In this lesson you have learned how to prove the Pythagorean Theorem by using squares and triangles.

11. Let’s Review Guided Practice Substitute the lengths of the sides of the triangle into the Pythagorean theorem and simplify to prove the Pythagorean Theorem.

12. Let’s Review Extension Activities 1. What type of triangle proves the Pythagorean Theorem?

13. Let’s Review Extension Activities Substitute the lengths of the sides of the triangle into the Pythagorean Theorem and simplify to prove the Pythagorean Theorem.

14. Let’s Review Extension Activities Explain why the drawing at the right is an illustration of the Pythagorean Theorem.

15. Let’s Review Quick Quiz 1. What are the two different formulas that we can use for the Pythagorean Theorem?

16. Let’s Review Quick Quiz 2. Substitute the lengths of the sides of the triangle into the Pythagorean Theorem and simplify to prove the Pythagorean Theorem.