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## PowerPoint Slideshow about ' 8 th Grade Math' - marvel

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Presentation Transcript

Warm-Up: Answers

Find the areas of the following:

1. 2. 3.

4. 5. What operation could be applied to the area in #5 to get the side length of the square?

A = 2 square units

A = 1 square unit

A = 4 square units

A = 5 square units

A = 1 square unit

So, to find the diagonal distance between two points, you can …

- Draw a line segment between the points.
- Make a square with the segment as a side.
- Find the area of the square.
- Take the square root of the area.

Do We Have to Make the Square Each Time?

If we remember our original line segment …

is the hypotenuse of

and we call the side lengths a, b, and c …

a2

c

b

a

+

=

b2

c2

That is, we can find …

the square of the hypotenuse

by adding

the squares of the legs

c2

b2

a2

This fact is known as the Pythagorean Theorem!

the hypotenuse

a2 + b2 = c2

152 + 202 = x2

225 + 400 = x2

625 = x2

25 = x

Using the Pythagorean Theoremx

15

20

a leg

a2 + b2 = c2

62 + x2 = 102

36 + x2 = 100

-36-36

x2 = 64

x = 8

Using the Pythagorean Theorem10

6

x

Looking for the diagonal distance

a2 + b2 = c2

32 + 42 = x2

9 + 16 = x2

25 = x2

5 = x

Using the Pythagorean Theoremx

3

4

HW (Front & Back of the Same WS)

- Applications #1-2, 5-6 (circled)
- Using the Pythagorean Theorem in Word Problems #1 (circled)

Warm-Up: Answers

Find the areas of the following:

1. 2. 3.

4. 5. What operation could be applied to the area in #5 to get the side length of the square?

A = 2 square units

A = 1 square unit

A = 4 square units

A = 5 square units

A = 1 square unit

So, to find the diagonal distance between two points, you can …

- Draw a line segment between the points.
- Make a square with the segment as a side.
- Find the area of the square.
- Take the square root of the area.

Do We Have to Make the Square Each Time?

If we remember our original line segment …

is the hypotenuse of

and we call the side lengths a, b, and c …

a2

c

b

a

+

=

b2

c2

That is, we can find …

the square of the hypotenuse

by adding

the squares of the legs

c2

b2

a2

This fact is known as the Pythagorean Theorem!

the hypotenuse

a2 + b2 = c2

152 + 202 = x2

225 + 400 = x2

625 = x2

25 = x

Using the Pythagorean Theoremx

15

20

HW (Front & Back of the Same WS)

- Applications #1-2, 5-6 (circled)
- Using the Pythagorean Theorem in Word Problems #1 (circled)

Warm-Up: Answers

Find the areas of the following:

1. 2. 3.

4. 5. What operation could be applied to the area in #5 to get the side length of the square?

A = 2 square units

A = 1 square unit

A = 4 square units

A = 5 square units

A = 1 square unit

So, to find the diagonal distance between two points, you can …

- Draw a line segment between the points.
- Make a square with the segment as a side.
- Find the area of the square.
- Take the square root of the area.

Do We Have to Make the Square Each Time?

If we remember our original line segment …

is the hypotenuse of

and we call the side lengths a, b, and c …

a2

c

b

a

+

=

b2

c2

That is, we can find …

the square of the hypotenuse

by adding

the squares of the legs

c2

b2

a2

This fact is known as the Pythagorean Theorem!

the hypotenuse

a2 + b2 = c2

152 + 202 = x2

225 + 400 = x2

625 = x2

25 = x

Using the Pythagorean Theoremx

15

20

Looking for the diagonal distance

a2 + b2 = c2

32 + 42 = x2

9 + 16 = x2

25 = x2

5 = x

Using the Pythagorean Theoremx

3

4

HW (Front & Back of the Same WS)

- Applications #1-2, 5-6 (circled)
- Using the Pythagorean Theorem in Word Problems #1 (circled)

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