Isosceles Trapezoid

In Euclidean geometry, an isosceles trapezoid (isosceles trapezium in British English) is a trapezoid where the legs have equal length. It can also be defined as a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides, making it automatically a trapezoid. Some sources would qualify all this with the exception: "excluding rectangles." Two opposite sides (the bases) are parallel, the two other sides (the legs) are of equal length. The diagonals are also of equal length. The base angles of an isosceles trapezoid are equal in measure (there are in fact two pairs of equal base angles, where one base angle is the supplementary angle of a base angle at the other base).

Any non-self-crossing quadrilateral with exactly one axis of symmetry must be either an isosceles trapezoid or a kite. However, if crossings are allowed, the set of symmetric quadrilaterals must be expanded to include also the antiparallelograms, crossed quadrilaterals in which opposite sides have equal length. Every antiparallelogram has an isosceles trapezoid as its convex hull, and may be formed from the diagonals and non-parallel sides of an isosceles trapezoid. The isosceles trapezoid is also (rarely) known as a symtra because of its symmetry.