Diagonals of Rectangle are Equal
Let $ABCD$ be a rectangle.
The diagonals of $ABCD$ are $AC$ and $BD$.
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 $AC = BD$.