1. Help with a proof

Could I please get some help with the following?
Given a quadrilateral with points labeled sequentially A B C D with a line segment AC and a line sement BD in the interior noted at intersection by point E with the following givens: segment BC = segment CD and segment AB = segment AD

Prove that AC is perpendicular to BD I'm stuck!
thanks SO much for any help or hints

2. Hello, murphmath!

Given a quadrilateral $\displaystyle ABCD$ with diagonals $\displaystyle AC$ and $\displaystyle BD$ intersecting at point $\displaystyle E$,
with the following givens: $\displaystyle BC = CD$ and $\displaystyle AB = AD.$

Prove that $\displaystyle AC$ is perpendicular to $\displaystyle BD.$
We have a kite-shaped figure . . .
Code:
            A
*
* | *
*   |   *
D * - - + - - * B
*    |E   *
*   |   *
*  |  *
* | *
*|*
*
C

We are given: .$\displaystyle AB = AD,\;BC = CD$

Point $\displaystyle A$ is equidistant from $\displaystyle B$ and $\displaystyle D.$
Point $\displaystyle C$ is equidistant from $\displaystyle B$ and $\displaystyle D.$

Hence, $\displaystyle AC$ is the perpendicular bisector of $\displaystyle BD.$

. . Therefore: .$\displaystyle AC \perp BD$