1. Holt McDougal Geometry 7-3-ext Providing the Pythagorean Theorem 7-3-ext Providing the Pythagorean Theorem Holt Geometry Lesson Presentation Lesson Presentation Holt McDougal Geometry

2. 7-3-ext Providing the Pythagorean Theorem Prove the Pythagorean Theorem using similar Triangles. Objectives

3. Holt McDougal Geometry 7-3-ext Providing the Pythagorean Theorem The Pythagorean Theorem is one of the most widely used and well-known mathematical theorems. The theorem has been proven in many different ways, some of which involve subdividing the triangle in some way. The following proof uses similar triangles.

4. Holt McDougal Geometry 7-3-ext Providing the Pythagorean Theorem Example 1:Proving the Pythagorean Theorem Using Similar Triangles For the figure, find b, c, and f.

5. Holt McDougal Geometry 7-3-ext Providing the Pythagorean Theorem Example 1: Continued Find b: Find f: 32 2 + 24 2 = b 2 1024 + 576 = b 2 1600 = b 2 40=b f 2 + 24 2 = 30 2 f 2 + 576 = 900 f 2 = 324 f = 18

6. Holt McDougal Geometry 7-3-ext Providing the Pythagorean Theorem Example 1: Continued Find c: c = 32 + f c = 32 + 18 c = 50

7. Holt McDougal Geometry 7-3-ext Providing the Pythagorean Theorem Check It Out! Example 1 In the figure, find c, e, and f. Find e: e 2 + 12 2 = 20 2 e 2 + 144 = 400 e 2 = 256 e = 16

8. Holt McDougal Geometry 7-3-ext Providing the Pythagorean Theorem Check It Out! Example 1 Continued Find f: Find c: f 2 + 12 2 = 15 2 f 2 + 144 = 225 f 2 = 81 f = 9 c = e + f c = 16 + 9 c = 25

9. Holt McDougal Geometry 7-3-ext Providing the Pythagorean Theorem Example 2: Applying the Pythagorean Theorem Megan, Tia, and Carla are running a relay race. Megan runs the first leg, 6.5 miles northwest. Tia runs the second leg, 4.0 miles south. How far east does Carla need to run to complete the race?

10. Holt McDougal Geometry 7-3-ext Providing the Pythagorean Theorem Example 2 : Continued Carla needs to run about 5.1 miles. a 2 + b 2 = c 2 4 2 + b 2 = 6.5 2 16 + b 2 = 42.25 b 2 = 26.25 b 5.1 ~ ~

11. Holt McDougal Geometry 7-3-ext Providing the Pythagorean Theorem Check It Out! Example 2 Jackie drives 5 miles east and 3 miles north from home to school. What is the shortest distance from Jackie’s home to school? The school is approximately 5.8 miles from her home. a 2 + b 2 = c 2 5 2 + 3 2 = c 2 25 + 9 = c 2 34 = c 2 c 5.8 ~ ~