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

Holt McDougal Geometry

7-3-ext Providing the Pythagorean Theorem7-3-ext Providing the Pythagorean Theorem

Holt Geometry

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Holt McDougal Geometry

Holt McDougal Geometry

7-3-ext Providing the Pythagorean Theorem

Prove the Pythagorean Theorem using similar Triangles.

Objectives

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.

Holt McDougal Geometry

7-3-ext Providing the Pythagorean TheoremExample 1:Proving the Pythagorean Theorem Using Similar Triangles

For the figure, find b, c, and f.

Holt McDougal Geometry

7-3-ext Providing the Pythagorean Theorem

Example 1: Continued

Find b:

Find f:

322 + 242 = b2

1024 + 576 = b2

1600 = b2

40=b

f2 + 242 = 302

f2 + 576 = 900

f2 = 324

f = 18

Holt McDougal Geometry

7-3-ext Providing the Pythagorean Theorem

Example 1: Continued

Find c:

c = 32 + f

c = 32 + 18

c = 50

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:

e2 + 122 = 202

e2 + 144 = 400

e2 = 256

e = 16

Holt McDougal Geometry

7-3-ext Providing the Pythagorean Theorem

Check It Out! Example 1 Continued

Find f:

Find c:

f2 + 122 = 152

f2 + 144 = 225

f2 = 81

f = 9

c = e + f

c = 16 + 9

c = 25

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?

Holt McDougal Geometry

7-3-ext Providing the Pythagorean Theorem

Example 2 : Continued

Carla needs to run about 5.1 miles.

a2 + b2 = c2

42 + b2 = 6.52

16 + b2 = 42.25

b2 = 26.25

b 5.1 ~~

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.

a2 + b2 = c2

52 + 32 = c2

25 + 9 = c2

34 = c2

c 5.8~~