First, can you show that triangles AEB and CED are congruent? This means that AB = CD.
Next, a little tougher. Can you show that triangles AED and AEB are congruent? This means that AB = AD.
Similar to the first problem, show that triangles AED and CEB are congruent. Thus AD = CB.
Putting it all together gives AB = BC = CD = DA. So we have a quadrilateral such that all sides are equal. What kind of quadrilateral is this?
I can't get the image to upload. Here's a quick rundown. I've got a quadrilateral ABCD. I have diagonals AC and BD meeting at right angles at a point E. The diagonals are bisected so we know that BE = ED and AE = EC.