The diagonals divide each other into segments with lengths that are pairwise equal in terms of the picture below, AE = DE, BE = CE (and AE ≠ CE if one wishes to exclude rectangles).Opposite angles are supplementary, which in turn implies that isosceles trapezoids are cyclic quadrilaterals.The segment that joins the midpoints of the parallel sides is perpendicular to them.An isosceles triangle is formed by the base and the extensions of the legs.If a quadrilateral is known to be a trapezoid, it is not necessary to check that the legs have the same length in order to know that it is an isosceles trapezoid any of the following properties also distinguishes an isosceles trapezoid from other trapezoids: Įxamples of isosceles trapezoids are rectangles and squares. The isosceles trapezoid is also (rarely) known as a symtra because of its symmetry. 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. 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. 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).Īny non-self-crossing quadrilateral with exactly one axis of symmetry must be either an isosceles trapezoid or a kite. 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. 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. In Euclidean geometry, an isosceles trapezoid ( isosceles trapezium in British English) is a trapezoid where the legs have equal length. An isosceles trapezoid and its axis of symmetry.