Properties of Trapezium

• The areas S and T of some two opposite triangles of the four triangles formed by the diagonals satisfy the equation

where K is the area of the quadrilateral.

• It has two adjacent angles that are supplementary, that is, they add up to 180 degrees.

• The angle between a side and a diagonal is equal to the angle between the opposite side and the same diagonal.

• The diagonals cut each other in mutually the same ratio (this ratio is the same as that between the lengths of the parallel sides).

• The diagonals cut the quadrilateral into four triangles of which one opposite pair are similar.

• The diagonals cut the quadrilateral into four triangles of which one opposite pair have equal areas.
• The consecutive sides a, c, b, d and the diagonals p, q satisfy the equation.