Special Polygons:

Triangle : A triangle is a three-sided polygon.
     The midsegment of a triangle is equal to 1/2 the base and is pararellel to the base.
     The three midsegments of a triangle devide the triangle into four congruent triangles.

Rectangle : A quadrilateral with all angles as right angles.
     The diagonals of rectangle are congruent.

: A rectangle with all congruent sides.

:  A quadrilateral with exactly two pairs of distinct congruent consecutive sides.
      The diagonals of a kite are perpendicular.
      The diagonal connecting the vertex angles of a kite is the perpendicular bisector of the other diagonal.
      The nonvertex angles of a kite are congruent.
      A diagonal bisects the vertex angles of a kite.

Trapezoid : A quadrilateral with exactly one pair of parallel sides.
      Consecutive angeles between the bases of a trapezoid are supplementary.
      An isosceles trapezoid is a trapezoid whose two non-parallel sides is the same length.
      The base angles of an isoceles triangle are congruent.
      The diagonals of an isosceles trapezoid are congruent.
      The midsegment of a trapezoid is equal in length to the average of the two bases and is parallel to the base.

Parallelogram : A quadrilateral whose opposite sides are parallel.
      The opposite sides of a parallelogram are congruent.
      Consecutive angles in a parallelogram are supplementary.
      Opposite angles in a parallelogram are congruent.
      The diagonals of a parallelogram bisect each other.

Rhombus : A parallelogram with all four sides congruent.
      The diagonals of a rhombus are perpendicular bisectors of each other.
      The diagonals of a rhombus bisect the angles of the rhombus.

Here is a Venn Diagram to help catagorize the different Quadrilateral:

* An apothem is the perpendicular distance from the center of a polygon's circumscribed circle to one of it's sides.