Course 3

4-8 The Pythagorean Theorem

Warm Up 2-16-09Estimate the value of each to the nearest tenth.

1. √30

2. √14

3. √55

4. √48

5.4 or 5.5

3.7 or 3.8

7.4 or 7.5

6.9

Course 3

4-8 The Pythagorean Theorem

Learn to use the Pythagorean Theorem and its converse to solve problems.

Course 3

The Pythagorean Theorem

Course 3

4-8 The Pythagorean Theorem

Pythagorean Theorem

leg

hypotenuse

Vocabulary

Course 3

4-8 The Pythagorean Theorem

Pythagoras was born on the Aegean island of Samos. He is best known for the Pythagorean Theorem, which relates the side lengths of a right triangle.

Course 3

4-8 The Pythagorean Theorem

Course 3

4-8 The Pythagorean Theorem

Directions: Find the leg of the hypotenuse to the nearest tenth.

Course 3

4-8 The Pythagorean Theorem

15 = c

Pythagorean TheoremSubstitute for a and b.

a2 + b2 = c2

92 + 122 = c2

81 + 144 = c2

225 = c

Simplify powers.

Solve for c; c = c2.

Example 1

Find the length of each leg first.

2225 c

Course 3

4-8 The Pythagorean Theorem

4

5

c

6.4 c

Pythagorean TheoremSubstitute for a and b.

a2 + b2 = c2

42 + 52 = c2

16 + 25 = c2

41 = c

Simplify powers. Solve for c; c = c2.

Example 2

41 = c2

Course 3

4-8 The Pythagorean Theorem

Example 3

5

7

c

8.6 c

Pythagorean TheoremSubstitute for a and b.

a2 + b2 = c2

52 + 72 = c2

25 + 49 = c2

74 = c

Simplify powers. Solve for c; c = c2.274 c

Course 3

4-8 The Pythagorean Theorem

Example 4

25

7

b

Find the positive square rootb = 24

a2 + b2 = c2

72 + b2 = 252

49 + b2 = 625–49 –49

b2 = 576

Pythagorean TheoremSubstitute for a and c. Simplify powers. Subtract 49 from each side.

576b

Course 3

4-8 The Pythagorean Theorem

Example 5

b 11.3

12

4

ba2 + b2 = c2

42 + b2 = 122

16 + b2 = 144–16 –16

b2 = 128

Find the positive square root.

Pythagorean TheoremSubstitute for a and c. Simplify powers.

Subtract 16 from both sides.

128b

Course 3

4-8 The Pythagorean Theorem

Directions: Determine whether or not the given numbers are

possible measures for the sides of a right triangle.

Course 3

4-8 The Pythagorean Theorem

Example 6

a = 3, b=4 and c = 5

Course 3

4-8 The Pythagorean Theorem

Example 7

7a

8b14c

Course 3

4-8 The Pythagorean Theorem

Lesson Summary

1. Find the height h of the triangle.

2. Find the length of side c to the nearest meter.

3. An escalator in a shopping mall is 40 ft long and 32 ft tall. What distance does the escalator carry shoppers?

8 m

12 m h

c10 m

6 m 9 m

Use the figure for Problems 1 and 2.

2624 ≈ 51 ft