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Objective

Find length using the Pythagorean Theorem

Vocabulary

Leg

Either of the two sides that form the right angle of a right triangle

legs

Vocabulary

Hypotenuse

The side opposite the right angle in a right triangle

Hypotenuse

Vocabulary

Pythagorean Theorem

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of

the lengths of the legs

C2 = A2 + B2Hypotenuse Legs

Vocabulary

Right triangle

A triangle with exactly one angle that measures 900

Example 1 Find the Length of the Hypotenuse

Example 2 Find the Length of a Leg

Example 3 Solve a Real-Life Problem

Example 4 Identify Right Triangles

Example 5 Identify Right Triangles

GYMNASTICS A gymnastics tumbling floor is in the shape of a square with sides 12 meters long. If a gymnast flips from one corner to the opposite corner, about how far has he flipped?

Draw the picture

Draw the right angle

Remember: The legs come off the right angle

The hypotenuse is the diagonal (the longest side)

To solve, find the length of the hypotenuse c.

Write Pythagorean Theorem

Replace a with 12

Evaluate

Add.

and b with 12.

1/5

Do the inverse on both sides of the equal sign

Answer:

Ask what is being done to the variable

The variable is being squared

c c = 16.97

1/5

The inverse of squaring is the square root

Find the square root of c2 (c c = c2)

Find the square root of 288

Add dimensional analysis

c = 16.97

Answer:c = 16.97

1/5

Add dimensional analysis

meters

SEWING Rose has a rectangular piece of fabric measuring 28 inches in length and 16 inches in width. She wants to decorate the fabric with a piece of lace sewn across both diagonals. How much lace will Rose need to complete the project?

Answer: c = 64.50 inches

Draw picture and label dimensions before solving

1/5

Find the missing measure of the triangle below.

Write the Pythagorean Theorem

Replace b with 9

Replace c with 15.

2/5

Do the inverse on both sides of the equal sign

Ask “what is being done to the variable?”

The variable is being added by 81

2/5

Find 152

255 =

Find 92

a2 + 81

2/5

Bring down 255

255 = a2 + 81

255

Subtract 81

- 81

Bring down = a2 + 81

= a2 + 81

Subtract 81

- 81

Combine “like” terms

144

Bring down = a2

= a2

Combine “like” terms

+ 0

2/5

Use the Identity Property to add a2 + 0

255 = a2 + 81

255 - 81 = a2 + 81 - 81

144 = a2 + 0

144 = a2

Ask “what is being done to the variable?”

The variable is being squared

Do the inverse on both sides of the equal sign

Find the square root of both sides of the equal sign

2/5

Find the square root of 144

255 = a2 + 81

255 - 81 = a2 + 81 - 81

144 = a2 + 0

144 = a2

12 =

Find the square root of a2

a

Add dimensional analysis

cmAnswer:

Find the missing measure of the triangle below. Round to the nearest hundredth if necessary.

Answer: a = 18.73 in.

Draw the picture before solving

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TELEVISION Televisions are measured according to their diagonal measure. If the diagonal of a television is 36 inches, and its height is 21.6 inches, what is its width?

3/5

Draw the picture before solving

Include the dimensions of each leg and the diagonal

Write the Pythagorean Theorem

3/5

Since c is the diagonal replace c with 36

A is the height of the TV so replace a with 21.6

3/5

B is the width of the TV so define your variable as b

3/5

Find 362

1,296 =

Find 21.62

466.56

Bring down + b2

+ b2

Ask “what is being done to the variable?”

The variable is being added by 466.56

Do the inverse on both sides of the equal sign

3/5

Bring down 1,296

1,296 = 466.56 + b2

1,296

Subtract 466.56

- 466.56

Bring down = 466.56

= 466.56

Subtract 466.56

- 466.56

Bring down + b2

+ b2

3/5

Combine “like” terms

1,296 = 466.56 + b2

1,296 - 466.56 = 466.56 - 466.56 + b2

829.44

Bring down =

=

Combine “like” terms

0 + b2

Use the Identity Property to add 0 + b2

829.44 = b2

Ask “what is being done to the variable?”

The variable is being squared

Find the square root of both sides of the equal sign

3/5

1,296 = 466.56 + b2

1,296 - 466.56 = 466.56 - 466.56 + b2

829.44 = 0 + b2

829.44 = b2

Find the square root of 829.44

Find the square root of b2

28.80 = b

Add dimensional analysi

In.

Answer:

SWIMMING The diagonal of a rectangular swimming pool measures 60 feet. Find the length of the pool if the width measures 30 feet. Round to the nearest hundredth if necessary.

Answer: b = 51.96 ft

3/5

Determine whether a triangle with the lengths 2.5 centimeters, 6 centimeters, and 6.5 centimeters is a right triangle.

Write the Pythagorean Theorem

Remember c is the longest side so replace c with 6.5

A is the shortest side so replace a with 2.5

4/5

6.52 = 2.52 +

B is the remaining leg so replace b with 6

62

Determine whether a triangle with the lengths 2.5 centimeters, 6 centimeters, and 6.5 centimeters is a right triangle.

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6.52 = 2.52 + 62

Find 6.52

42.25

Find 2.52

= 6.25Find 62

+ 36Combine “like” terms

42.25 = 42.25Both sides of the equal sign have the same value

If both are equal, then the triangle is a right triangle

Answer: The triangle is a right triangle.

Determine whether a triangle with the lengths 5 inches, 12 inches, and 13 inches is a right triangle.

Answer: the triangle is a right triangle

4/5

Determine whether a triangle with the lengths 5 feet, 6 feet, and 8 feet is a right triangle.

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Write the Pythagorean Theorem

Remember c is the longest side so replace c with 8

82 =

A is the shortest side so replace a with 5

52 +

B is the remaining leg so replace b with 6

62

Determine whether a triangle with the lengths 5 feet, 6 feet, and 8 feet is a right triangle.

5/5

82 = 52 + 62

Find 82

64 =

Find 52

25 +

Find 62

36 Combine “like” terms

64 = 61 Both sides of the equal sign do not have the same value

Since both sides are not equal, it cannot be a right triangle

Answer: It is not a right triangle

Determine whether a triangle with the lengths 4.5 centimeters, 9 centimeters, and 12.5 centimeters is a right triangle.

Answer: It is not a right triangle

5/5

Lesson 11:3 The Pythagorean Theorem 9 - 21 All

Assignment