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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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8 th Grade Math

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8th Grade Math

1st 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?

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.


But …

Do We Have to Make the Square Each Time?


No! Notice that …

=

making

+

=


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!


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)


8th Grade Math

2nd 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?

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.


But …

Do We Have to Make the Square Each Time?


No! Notice that …

=

making

+

=


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!


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)


8th Grade Math

4th 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?

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.


But …

Do We Have to Make the Square Each Time?


No! Notice that …

=

making

+

=


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!


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)


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