The Square - The four sides of a square are all equal. The four angles are each 90°. If you join a diagonal of a square you will create two equal triangles.
The Rectangle - Opposite sides of a rectangle are of equal length. The four angles are each 90°. The diagonal bisects the area of a rectangle into two equal triangles.
The Rhombus - The four sides of a rhombus are equal in length, opposite sides are parallel and opposite angles are equal.
If you joined the diagonals of a Rhombus they will bisect each other at 90°. See directly below to experiment with this fact for yourself.
The Rhomboid or Parallelogram
The Rhomboid or Parallelogram - The opposite sides of a rhomboid are parallel and equal in length. The opposite angles are equal. The diagonal bisects the area of the Rhomboid into two equal triangles.
The Trapezium - A Trapezium has two parallel sides.
The Trapezoid - A Trapezoid has no equal or parallel sides.