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 is a right triangle?

• A triangle with all sides equal

• A triangle with one angle greater than 90 degrees

• A triangle with one right angle

• A triangle with all angles less than 90 degrees

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

• Divide the side length by two

• Multiply the side length by two

• Add the side lengths together

• Multiply the side length by itself

What is the area of a tilted square with congruent legs?

• It is equal to the area of a non-tilted square

• It is always zero

• There is no square when the legs are congruent

• It is double the area of a non-tilted square

In the first example, what is the area of the square extending from the hypotenuse?

• 1 square unit

• 2 square units

• 3 square units

• 4 square units

In the second example, what is the area of the square extending from leg two?

• 4 square units

• 3 square units

• 1 square unit

• 2 square units

What does the Pythagorean theorem state about the areas of squares on a right triangle?

• The area of the hypotenuse square is equal to the sum of the other two

• The area of the hypotenuse square is unrelated to the other two

• The area of the hypotenuse square is less than the sum of the other two

• The area of the hypotenuse square is more than the sum of the other two

How is the Pythagorean theorem expressed algebraically?

• a + b^2 = c^2

• a^2 + b^2 = c

• a^2 + b^2 = c^2

• a^2 + b = c^2