Question

Prove that in a rectangle ABCD the diagonals are equal.

Answer 1

Since rectangles have right angles in each corner and opposite sides of a rectangle are congruent, then in rectangle ABCD it would be true that AB is congruent to CD.

Therefore by the Pythagorean Theorem: AB² + BC² = AC² and CD² + BC² = BD²

But since AB = CD, it follows that AB² = CD²

So AB² + BC² = CD² + BC²

∴ AC² = BD²

⇒ AC= BD

Hence, diagonals are of equal length.