Pythagorean Theorem

Pythagorean Theorem

Reviewing important information needed for Trigonometry

The Pythagorean Theorem

• Can only be used on RIGHT triangles (meaning it has a 90^oangle)

•  $a^2+b^2=c^2$  

• In other words, if you square the two legs of a triangle and add those amounts together, the sum is equal to the square of the hypotenuse.

Hypotenuse

• The longest side of a right triangle

• The side that is opposite (across) from the 90^o angle.

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

Fill in the Blank

How long is the hypotenuse of this triangle?

Leg (of a Triangle)

• The two shorter sides of a right triangle

• The sides that are adjacent to the 90^o angle.

• When using the Pythagorean Theorem, the Legs are represented by the variables, a & b.

Right Triangle

• A right triangle is a triangle with a right angle in it (an angle that is 90^o)

• A triangle can be shown to have a 90^o angle by using a box.

• A right triangle will ALWAYS satisfy the Pythagorean Theorem

•  $a^2+b^2=c^2$  

Is it a Right Triangle?

• We can tell if a triangle is a right triangle by plugging in the lengths of a triangle into the Pythagorean Theorem. If it's true, then that means it IS a right triangle.

•  $a^2+b^2=c^2$  

•  $15^2+20^2=25^2$  

•  $225+400=625$  

•  $625=625$  

• This IS a right triangle!

Multiple Choice

Is this a right triangle?

• Yes

• No

Multiple Choice

Is this a right triangle?

• Yes

• No

Multiple Choice

Is this a right triangle?

• Yes

• No

Multiple Choice

Is a triangle with side lengths of 12, 9, and 15 a right triangle?

• Yes

• No

Multiple Choice

Is a triangle with side lengths of 7, 4, and 4 a right triangle?

• Yes

• No

Multiple Choice

Find the missing side.

• 18

• 16

• 17

• 19

Multiple Choice

Find the missing side.

• 11

• 12

• 13

• 14

Multiple Choice

A triangle has legs that are 7 inches and 24 inches long. How long is the hypotenuse?

• 23

• 26

• 28

• 25