A quadrilateral is a polygon that has four sides.

Special Types of Quadrilaterals

• Parallelogram
• A parallelogram is a quadrilateral having two pairs of parallel sides.
• The two opposite sides are equal.
• Opposite angles are equal.
• Rhombus
• A rhombus is a quadrilateral of which all four sides are the same length.
• Rectangle
• A rectangle is a parallelogram of which all four angles are 90 degrees.
• Square
• A square is a quadrilateral of which all four sides are of the same length, and all four angles are 90 degrees.
• Trapezoid
• A trapezoid is a quadrilateral which has two parallel sides (U.S.)
• Trapezium
• U.S. usage: A trapezium is a quadrilateral which has no parallel sides.
• U.K usage: A trapezium is a quadrilateral with two parallel sides (same as US trapezoid definition).
• Kite
• A kite is an quadrilateral with two pairs of congruent adjacent sides.

One of the most important properties used in proofs is that the sum of the angles of the quadrilateral is always 360 degrees. This can easily be proven too:

If you draw a random quadrilateral, and one of its diagonals, you'll split it up into two triangles. Given that the sum of the angles of a triangle is 180 degrees, you can sum them up, and it'll give 360 degrees.