Special Qualities of Quadrilaterals

1. Parallelogram:

   • A quadrilateral with opposite sides parallel and equal in length.

   • Opposite angles are equal.

   • The diagonals bisect each other.

   • The sum of adjacent angles is 180 degrees.

   • Each diagonal divides the parallelogram into two congruent triangles.

2. Square:

   • A special type of parallelogram that has all sides equal and all angles measuring 90 degrees.

   • A square is both a rhombus (equal sides) and a rectangle (equal angles).

   • The diagonals are equal in length, bisect each other at right angles, and are also congruent.

   • Diagonals divide the square into four congruent right triangles.

3. Rhombus:

   • A parallelogram with all sides of equal length.

   • Opposite angles are equal and adjacent angles are supplementary.

   • The diagonals bisect each other at right angles and are not necessarily equal.

   • Each diagonal divides the rhombus into two congruent triangles.

4. Trapezoid:

   • A quadrilateral with at least one pair of parallel sides.

   • The angles adjacent to each leg (non-parallel side) are supplementary.

   • The median of a trapezoid is parallel to the bases and its length is the average of the lengths of the two bases.

5. Isosceles Trapezoid:

   • A trapezoid where the non-parallel sides (legs) are of equal length.

   • The angles at each base are equal.

   • The diagonals are of equal length.

   • The median is parallel to the bases and its length is the average of the two bases.

6. Kite:

   • A quadrilateral with two distinct pairs of adjacent sides that are equal.

   • The diagonals intersect at a right angle.

   • One of the diagonals bisects the angles of the other diagonal.

   • Opposite angles are equal where the diagonals intersect.