Lesson 8-7 The Pythagorean Theorem

1. Lesson 8-7The Pythagorean Theorem The Py-tha’-go-rean Thee’uh-rem (named after Pythagoras)

2. Building squares on right angles

3. Pythagorean theorem In any right triangle, the sum of the squares of the lengths a and b of the legs is equal to the square of the length c of the hypotenuse.

4. c2 = a2 + b2 Pythagorean Theorem c2 = 212 + 202 Substitute. c2 = 441 + 400 Simplify. c2 = 841 c2 = 841 Take the square root of each side. c = 29 The Pythagorean Theorem LESSON 8-7 Additional Examples Find the length of the hypotenuse. The length of the hypotenuse is 29 in. 8-7

5. a2 + b2 = c2 Pythagorean Theorem a2 + 152 = 252 Substitute. a2 + 225 = 625 Simplify. a2 + 225 – 225 = 625 – 225 Subtract 225 from both sides. a2 = 400 Simplify. a2 = 400 Take the square root of each side. a = 20 The Pythagorean Theorem LESSON 8-7 Additional Examples Find the missing leg of the triangle. The length of the leg is 20 ft. 8-7

6. 8.7: Applying the Pythagorean theorem

7. Objective We use Pythagorean theorem to solve real-world situations Sometimes, a triangle is not obvious but you can visualize the sides of a triangle and then draw a picture Now, let’s work on a word problem.

8. Draw a diagram to illustrate the problem. Use the Pythagorean Theorem. Use the Pythagorean Theorem. c2 = a2 + b2 c2 = 42 + 11.32 Substitute. c2 = 16 + 127.69 Square 4 and 11.3. c2 = 143.69 Add. Take the square root of each side. c2 = 143.69 c = 11.98708 Use a calculator. The Pythagorean Theorem LESSON 8-7 Additional Examples A ladder, placed 4 ft from a wall, touches the wall 11.3 ft above the ground. What is the approximate length of the ladder? The length of the ladder is about 12 ft. 8-7

9. Homework Lesson 8-7 pp. 407-408 #s 1-10, 15-18, 22-24 (Can use a calculator if c2 is not a perfect square) Complete Activity Lab if needed.