Pythagorean Theorem (8th Math)

The Pythagorean Theorem

The Pythagorean Theorem is used to find the unknown side measure in a right triangle. You may remember the Pythagorean Theorem from Geometry.

Poll

The formula for the Pythagorean Theorem is below. Does this formula seem familiar to you?  

 $a^2+b^2=c^2$  

• Yes!

• A little bit

• Not at all!

Poll

How do you feel about Pythagorean theorem at this point?

• Great, I could teach it to someone

• Good, I still have a few questions

• I am very confused and I don't no where to start

Parts of a Right Triangle

• Hypotenuse - Side across from (opposite) the right angle

• Legs - The other 2 sides

Hypothenuse

• The longest side of a right triangle

• The side of a right triangle that is opposite from the 90 degree angle

• When using the Pythagorean Theorem, the Hypotenuse is represented by the variable c

• This length is less than the sum of the length of the legs

Multiple Choice

Which side is the hypotenuse in this right triangle?

• 5

• 12

• 13

Multiple Choice

What is the hypothenuse of this right triangle?

• 13

• 12

• 5

Pythagorean Theorem

The area of the square whose side is the hypotenuse(diagonal) is equal to the sum of the areas of the squares on the other two sides.

 $a^2+b^2=c^2$  

Label your sides a, b, and c

• the hypothenuse c is the longest side

• c is the side of a right triangle that is opposite from the 90 degree angle

• a and b are the legs

Multiple Choice

Substitute your values to the theorem

• $a^2+6^2=8^2$

• $8^2+6^2=c^2$

• $8^2+b^2=6^2$

Solve for the missing length

You must take the square root to get the length side.

Multiple Choice

Solve the problem on your paper and type your answer in. #1 Find the Missing Side.

 $a^2+b^2=c^2$  

• c=18

• c=16

• c=17

• c=19

Multiple Choice

A triangle has legs that are 7 in and 24 in long. How long is the hypothenuse?

• 23

• 26

• 28

• 25

Label your sides a, b, and c

Type in chat what the side lengths are.

Multiple Choice

Substitute your values to the theorem

•  $a^2+12^2=20^2$ 

•  $20^2+12^2=c^2$ 

Multiple Choice

Solve the problem on your paper and type your answer in. #2 Find the Missing Side

• b=11

• b=12

• b=13

• b=14

Fill in the Blank

Solve for the missing side of the right triangle. Round to the nearest tenth.

Fill in the Blank

Solve for the missing side of the right triangle. Round to the nearest tenth.