Using the Area of Squares Proof to Relate Side Lengths of a Right Triangle

This lesson explains the relationship between the side lengths of a right triangle using the area of squares proof. It begins with a review of right triangle properties, then explores how to find the area of tilted and non-tilted squares. The lesson demonstrates how to calculate the areas of squares extending from the legs and hypotenuse of right triangles, leading to the discovery of the Pythagorean theorem. Through examples, it shows that the sum of the areas of the squares on the legs equals the area of the square on the hypotenuse, reinforcing the theorem's validity.

What defines a right triangle?

How do you find the area of a non-tilted square?

Explain how to find the area of a tilted square.

What is the relationship between the areas of the squares extending from the legs and the hypotenuse of a right triangle?

What conclusion can be drawn from the examples provided regarding the areas of squares in right triangles?

State the Pythagorean theorem.

How can the Pythagorean theorem be expressed using variables?