Pre-Algebra Q4W1: Pythagorean Theorem Objective: I can apply the Pythagorean Theorem to determine unknown side lengths in right triangles.

The Pythagorean applies only to right triangles The two sides that make up the right angle are called legs. The side opposite the right angle is the hypotenuse. It is always the longest side of the right triangle. leg hypotenuse right angle

3 4 5 About 2500 year’s ago, a Greek mathematician named Pythagorus realized that if you square the lengths of the two sides that make up the right angle and add them together, the sum is equal to the area of the longest side squared.

a a a2a2 b b c c b2b2 c2c2 Let’s look at it this way…

The Pythagorean Theorem a 2 + b 2 = c 2 Note: The hypotenuse, c, is always the longest side.

It is true for any right triangle

You can use The Pythagorean Theorem to solve many kinds of problems.

Example: Drive 3 miles west. Then turn south and drive for 4 miles. 3 4

3232 How Far are you from where you started? Using The Pythagorean Theorem: 3 4 c =c2c2

Pythagorean Theorem Steps 1.Square Each Side 2.Add (if you have both legs) or Subtract (if you are missing a leg) 3.Find the Square Root

Use the Pythagorean Theorem to solve for the missing side length.

You can use it to find the length of a diagonal of a rectangle: 15" 8"

Use the Pythagorean Theorem to solve for the missing side length.

Is this a right triangle?

Any set of 3 whole numbers that satisfies the Pythagorean Theorem a 2 +b 2 = c 2 Example: = 5 2 So is a Pythagorean Triple What is a Pythagorean Triple?

Pythagorean Triples You can make more Pythagorean Triples by “scaling them up.” Example: And so on.

Use the Pythagorean Theorem to find the distance between the two points.

Practice Worksheet