The diagonals of a rhombus have three special properties.
Recall that a rectangle is a parallelogram. It therefore has all the properties of a parallelogram. One more useful fact is true of rectangles, though. The diagonals of a rectangle are equal. This is true because rectangles are equiangular.
Now recall that a square is both a rhombus and a rectangle. Its sides and angles are all congruent. From this fact, it follows:
An isosceles trapezoid is the name given to a trapezoid with equal legs. The angles whose vertices are the vertices of the longer base are called the lower base angles, and the other two angles are called the upper base angles. For every isosceles trapezoid, the following is true:
One additional theorem applicable to all regular polygons must be mentioned. You have probably already assumed as much from drawings, but to make it official, we'll state it as a theorem: the radii of a regular polygon bisect the interior angles.
A final handy theorem with polygons has to do with perpendicular bisectors. The points on a perpendicular bisector are equidistant from the endpoints of the segment that they bisect.