# Pythagorean Theorem by Inductive Reasoning

- Author:
- Jennifer Talavage,

Enter your name.

## The red figure is a square.

**a**and

**b**and hypotenuse

**c**. Each side of the red square is a straight angle. The measure of a straight angle is 180, so x + y + z = 180. For each green triangle, x + z + 90 = 180.

1. Why is the magenta space a square?

2. Write an expression for the area of the magenta square in terms of c.

**Transform**slider to the right. The magenta space now appears as two squares, but the total area is the same as the area of the original magenta square before the transformation.

3. Write an expression for the area of the upper magenta square in terms of a.

4. Write an expression for the area of the lower magenta square in terms of b.

5. Write an expression for the total area of the magenta space in terms of a and b.

6. Now, set your expressions for the area of the magenta space from #2 and #5 equal to each other.

7. The **Pythagorean Theorem** states that the side lengths of a **right triangle** are related by the equation
**a ^{2} + b^{2} = c^{2}**, where

**a**and

**b**are

**legs**and

**c**is the

**hypotenuse**. Did this

**inductive reasoning**activity help convince you about the truth of the Pythagorean Theorem? Explain.