6-3

1 / 15

6-3 - PowerPoint PPT Presentation

6-3. The Pythagorean Theorem. Warm Up. Problem of the Day. Lesson Presentation. Course 3. 6-3. The Pythagorean Theorem. Course 3. Warm Up Graph the figures with the given vertices and find the area. 1. (–1, –1), (–1, 3), (6, –1) 2. (2, 1), (8, 1), (6, –3)

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

PowerPoint Slideshow about '6-3' - cuyler

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

6-3

The Pythagorean Theorem

Warm Up

Problem of the Day

Lesson Presentation

Course 3

6-3

The Pythagorean Theorem

Course 3

Warm Up

Graph the figures with the given vertices and find the area.

1. (–1, –1), (–1, 3), (6, –1)

2. (2, 1), (8, 1), (6, –3)

3. (3, –2), (15, –2), (14, 6), (4, 6)

14 units2

12 units2

88 units2

6-3

The Pythagorean Theorem

Course 3

Problem of the Day

A side of a square A is 5 times the length of square B. How many times as great is the area of square A than the area of square B?

25

6-3

The Pythagorean Theorem

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

Course 3

6-3

The Pythagorean Theorem

Course 3

Vocabulary

Pythagorean Theorem

leg

hypotenuse

6-3

The Pythagorean Theorem

a2 + b2 = c2

Course 3

6-3

The Pythagorean Theorem

41 = c

Solve for c; c = c2.

Course 3

Additional Example 1A: Find the the Length of a Hypotenuse

Find the length of the hypotenuse.

c

A.

4

5

Pythagorean Theorem

a2 + b2 = c2

42 + 52 = c2

Substitute for a and b.

Simplify powers.

16 + 25 = c2

41 = c2

6.40c

6-3

The Pythagorean Theorem

Solve for c; c = c2.

225 = c

Course 3

Additional Example 1B: Find the the Length of a Hypotenuse

Find the length of the hypotenuse.

triangle with coordinates

B.

(1, –2), (1, 7), and (13, –2)

Pythagorean Theorem

a2 + b2 = c2

Substitute for a and b.

92 + 122 = c2

Simplify powers.

81 + 144 = c2

15= c

6-3

The Pythagorean Theorem

74 = c

Solve for c; c = c2.

Course 3

Try This: Example 1A

Find the length of the hypotenuse.

c

A.

5

7

Pythagorean Theorem

a2 + b2 = c2

52 + 72 = c2

Substitute for a and b.

Simplify powers.

25 + 49 = c2

8.60c

6-3

The Pythagorean Theorem

y

x

Solve for c; c = c2.

61 = c

Course 3

Try This: Example 1B

Find the length of the hypotenuse.

B. triangle with coordinates (–2, –2), (–2, 4), and (3, –2)

(–2, 4)

The points form a right triangle.

a2 + b2 = c2

Pythagorean Theorem

62 + 52 = c2

Substitute for a and b.

36 + 25 = c2

Simplify powers.

(3, –2)

(–2, –2)

7.81c

6-3

The Pythagorean Theorem

576 = 24

Course 3

Additional Example: 2 Finding the Length of a Leg in a Right Triangle

Solve for the unknown side in the right triangle.

Pythagorean Theorem

a2 + b2 = c2

25

Substitute for a and c.

72 + b2 = 252

b

Simplify powers.

49 + b2 = 625

–49 –49

b2 = 576

7

b = 24

6-3

The Pythagorean Theorem

128  11.31

Course 3

Try This: Example 2

Solve for the unknown side in the right triangle.

a2 + b2 = c2

Pythagorean Theorem

12

Substitute for a and c.

b

42 + b2 = 122

Simplify powers.

16 + b2 = 144

–16 –16

4

b2 = 128

b 11.31

6-3

The Pythagorean Theorem

a = 20 units ≈ 4.47 units

1

2

1

2

A = hb = (8)( 20) = 4 20 units2 17.89 units2

Course 3

Additional Example 3: Using the Pythagorean Theorem to Find Area

Use the Pythagorean Theorem to find the height of the triangle. Then use the height to find the area of the triangle.

a2 + b2 = c2

Pythagorean Theorem

Substitute for b and c.

a2 + 42 = 62

a2 + 16 = 36

6

6

a

a2 = 20

4

4

Find the square root of both sides.

6-3

The Pythagorean Theorem

a = 21 units ≈ 4.58 units

1

2

1

2

A = hb = (4)( 21) = 2 21 units2 9.17 units2

Course 3

Try This: Example 3

Use the Pythagorean Theorem to find the height of the triangle. Then use the height to find the area of the triangle.

a2 + b2 = c2

Pythagorean Theorem

a2 + 22 = 52

Substitute for b and c.

5

5

a2 + 4 = 25

a

a2 = 21

2

2

Find the square root of both sides.

6-3

The Pythagorean Theorem

Course 3

Lesson Quiz

Use the figure for Problems 1-3.

1. Find the height of the triangle.

8 m

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

c

10 m

h

12 m

3. Find the area of the largest triangle.

6 m

9 m

60 m2

4. One leg of a right triangle is 48 units long, and the hypotenuse is 50 units long. How long is the other leg?

14 units