The Pythagorean Theorem

Pythagorean Theorem & It's Converse

The Pythagorean Theorem

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.

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

• undefined 

Is it a Right Triangle?

How to Solve

1. Determine what side is missing.

2. Plug in what you know into the equation.

3. Simplify the equation.

4. Solve for the missing side.

5. If needed round to the nearest tenth!

Copy this down

The Converse of the Pythagorean Theorem

If the sum of the squares of the legs in a triangle equal to the square of the hypotenuse then you have a right triangle.

Lets work one together

Multiple Choice

Find the missing side length.

• $$\sqrt[]{73}\ cm$$  

• $$\sqrt[]{17}\ \ cm$$  

• $$73\ \ cm$$  

• $$\sqrt[]{13}\ \ cm$$  

Multiple Choice

Find the missing side length.

• $$\sqrt[]{5}\ ft$$  

• $$\sqrt[]{493}\ ft$$  

• $$\sqrt[]{31}\ ft$$  

• $$\sqrt[]{155}\ ft$$  

Multiple Choice

Find missing side

• $$2\sqrt{5}$$

• $$\sqrt{20}$$

• $$2\sqrt{3}$$

Multiple Choice

Find the missing leg

• 57.6

• 66.1

• 60

Multiple Choice

Find the missing side.

• 9

• 10

• 12

• 100