Question

Rectangles: Depending on the previous responses, why are the diagonal measurements the same or different?

Answer 1

[AI-generated answer — Bot GPT 3.5]

The diagonal measurements of rectangles are always the same. This is because a rectangle is a parallelogram with congruent opposite sides. The diagonal of a rectangle forms a right triangle with the sides of the rectangle, and by the Pythagorean theorem, the diagonal length is equal to the square root of the sum of the squares of the two sides. Since the opposite sides of a rectangle are equal in length, the squares of their lengths are equal. Therefore, the sum of the squares of the two sides is the same, leading to the diagonal measurements also being the same.