Diagonals of Quadrilaterals

A diagonal of a polygon is created when two non-consecutive vertices are connected by a segment. See the image on the right below for an illustration.

In convex quadrilaterals, the diagonals can:
*be non-congruent
*be congruent
*bisect each other
*meet at right angles
Find all of the possible combinations of diagonals that can occur and construct the quadrilateral that they define.