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# 8 th Grade Math - PowerPoint PPT Presentation

8 th Grade Math. 1 st Period Nov . 1, 2012. No HW Review; Start Warm-Up. Find the areas of the following: 1. 2. 3. 4. 5. . 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?.

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Presentation Transcript

1st Period

Nov. 1, 2012

No HW Review; Start Warm-Up

Find the areas of the following:

1. 2. 3.

4. 5.

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

• 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.
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

the squares of the legs

c2

b2

a2

This fact is known as the Pythagorean Theorem!

Looking for length of

the hypotenuse

a2 + b2 = c2

152 + 202 = x2

225 + 400 = x2

625 = x2

25 = x

Using the Pythagorean Theorem

x

15

20

Looking for length of

a leg

a2 + b2 = c2

62 + x2 = 102

36 + x2 = 100

-36-36

x2 = 64

x = 8

Using the Pythagorean Theorem

10

6

x

Looking for the diagonal distance

a2 + b2 = c2

32 + 42 = x2

9 + 16 = x2

25 = x2

5 = x

Using the Pythagorean Theorem

x

3

4

HW (Front & Back of the Same WS)
• Applications #1-2, 5-6 (circled)
• Using the Pythagorean Theorem in Word Problems #1 (circled)

2nd Period

Nov. 1, 2012

No HW Review; Start Warm-Up

Find the areas of the following:

1. 2. 3.

4. 5.

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

• 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.
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

the squares of the legs

c2

b2

a2

This fact is known as the Pythagorean Theorem!

Looking for length of

the hypotenuse

a2 + b2 = c2

152 + 202 = x2

225 + 400 = x2

625 = x2

25 = x

Using the Pythagorean Theorem

x

15

20

HW (Front & Back of the Same WS)
• Applications #1-2, 5-6 (circled)
• Using the Pythagorean Theorem in Word Problems #1 (circled)

4th Period

Nov. 1, 2012

No HW Review; Start Warm-Up

Find the areas of the following:

1. 2. 3.

4. 5.

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

• 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.
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

the squares of the legs

c2

b2

a2

This fact is known as the Pythagorean Theorem!

Looking for length of

the hypotenuse

a2 + b2 = c2

152 + 202 = x2

225 + 400 = x2

625 = x2

25 = x

Using the Pythagorean Theorem

x

15

20

Looking for the diagonal distance

a2 + b2 = c2

32 + 42 = x2

9 + 16 = x2

25 = x2

5 = x

Using the Pythagorean Theorem

x

3

4

HW (Front & Back of the Same WS)
• Applications #1-2, 5-6 (circled)
• Using the Pythagorean Theorem in Word Problems #1 (circled)