# Discover Pythagorean Theorem

## Learning Goal

Students will explore relationships between squares and right triangles, and learn the Pythagorean Theorem.

## 'Hypotenuse Squares'

## Visual 1: Click and drag the points to explore the distance between them.

## Question 1: Use the Visual to...

Choose only ** ONE** set of points, and use the 'hypotenuse square' to find the distance between them.

- (-5, -2) and (3, 2)
- (-3, -3) and (0, -9)

**Hint:**Review the 'Hypotenuse Squares' figures and explanation above.

## Question 1: Check your answer.

## What's next?

Finding the distance between two points (or the length of the hypotenuse) is possible by finding the square root area of the 'hypotenuse square'. Now, we will look for a simpler way to find the area of this square.

## Visual 2: Click and drag the points to explore the patterns between the side lengths of a right triangle.

## Question 2: Use the Visual to...

List the 3 square areas for a right triangle with each set of side lengths.

- 3, 4, and 5 units
- 5, 12, and 13 units
- 6, 8, and 10 units

**Bonus:**Use the words leg and hypotenuse.

## Question 2: Check your answer.

## Visual 3: Click and drag the circles to move the area pieces.

## Question 3: Use the Visual to...

Describe what is happening in your own words.

## Question 3: Check your answer.

## What's next?

Finding the distance between two points (or the length of the hypotenuse) becomes more straightforward if we use the relationship between the squares of the sides of a right triangle.
This relationship is called

**The Pythagorean Theorem**and is often represented by this equation: , where and are the lengths of the legs (shorter sides) and is the length hypotenuse (longer side).## The Pythagorean Theorem

## Visual 4: Click and drag the points to explore the distance between them.

## Question 4: Use the Visual to...

Find the hypotenuse 'c' for each set of leg lengths ('a' & 'b').

- a = 1, b = 7, c = ?
- a = 9, b = 4, c = ?

**Hint:**Use the

**Pythagorean Theorem**, .