Which statement about the Proof of the Pythagorean Theorem is true?

Question

(1 point)
Responses

The sides of the squares are equal to the square of the areas.
The sides of the squares are equal to the square of the areas.

The sides of the right triangle in the center must have the relationship that the smaller two legs add to equal the longest side.
The sides of the right triangle in the center must have the relationship that the smaller two legs add to equal the longest side.

To make a right triangle in the center, the area of the smaller two squares must add to equal the area of the largest square.
To make a right triangle in the center, the area of the smaller two squares must add to equal the area of the largest square.

The area of the three squares that create a right triangle are always multiples of 3, 4, and 5.
The area of the three squares that create a right triangle are always multiples of 3, 4, and 5.

​​​​​​​Any three squares can be put together to create a right triangle in the center.

Answer 1

The correct statement about the Proof of the Pythagorean Theorem is:

To make a right triangle in the center, the area of the smaller two squares must add to equal the area of the largest square.

This statement captures the essence of the Pythagorean Theorem, which is expressed as \(a^2 + b^2 = c^2\) for a right triangle with legs \(a\) and \(b\), and hypotenuse \(c\). This means that the area of the square built on the two shorter sides (the legs) equals the area of the square built on the longest side (the hypotenuse).