An isosceles trapezoid (isosceles trapezium in British English) is a quadrilateral with a line of symmetry bisecting one pair of opposite sides, making it automatically a trapezoid. Two opposite sides (bases) are parallel, the two other sides (legs) are of equal length. The diagonals are of equal length. An isosceles trapezoid's base angles are congruent. Any quadrilateral with one axis of symmetry must be either an isosceles trapezoid or a kite.
Equal Segments of diagonals
The diagonals of an isosceles trapezoid are equal in length and divide each other into equal segments: and
Therefore the diangle length is
The area of an isosceles (or any trapezoid) is equal to the average of the bases times the height. In the diagram to the right, = segment , = segment and is the length of a line segment between AD and BC and perpendicular to them. The area is given as follows
Another equivalent formula for the area, which better resembles Heron's formula is:
where is the semiperimeter of the trapezoid.
The circumradius is
The inradius is