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