Diagonals of Rectangle are Equal

Theorem
The diagonals of a rectangle are equal.

Proof

 * Diagonals of Rectangle are Equal.png

Let $ABCD$ be a rectangle.

The diagonals of $ABCD$ are $AC$ and $BD$.

Then $\angle ADC = \angle DAB$ as both are right angles by definition of rectangle.

By Rectangle is Parallelogram, $ABCD$ is also a type of parallelogram.

Thus by Opposite Sides and Angles of Parallelogram are Equal $AB = DC$.

Thus we have:
 * $AB = DC$
 * $\angle ADC = \angle DAB$
 * $AD$ is common to both $\triangle ADC$ and $\triangle DAB$

and so by Triangle Side-Angle-Side Equality it follows that $\triangle ADC = \triangle DAB$.

Thus $AC = BD$.