Thread: Prove

Prove analytically the the diagonals of a rectangle are equal.

I really have no idea. Please help. Thanks!

there are so many ways to prove this

Here's the easiest one

Let's say you have a rectangle ABCD. AB is parallel to CD and BC is parallel to AD. And since rectangle has right angles it would be true that AB is congrudent to CD.
Therefore we can use a Pythagorean Theorem:

AB² + BC² = AC² and CD² + BC² = BD²

and since AB = CD -> AB² = CD² so

AB² + BC² = CD² + BC²
AB² + BC² = AB² + BC²
AC² = BD²

Simply prove in the rectangle the congruency of 2 right angled triangles (SAS)
the two hypotenuses of these triangles are actually the two diagonals of the rectangle.