In Euclidean geometry, an isosceles trapezoid is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides. It is a special case of a trapezoid. Alternatively, it can be defined as a trapezoid in which both legs and both base angles are of equal measure, or as a trapezoid whose diagonals have equal length. Note that a non-rectangular parallelogram is not an isosceles trapezoid because of the second condition, or because it has no line of symmetry. In any isosceles trapezoid, two opposite sides (the bases) are parallel, and the two other sides (the legs) are of equal length (properties shared with the parallelogram), and the diagonals 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).

A trapezoid is defined as a quadrilateral having exactly one pair of parallel sides, with the other pair of opposite sides non-parallel. However, the trapezoid can be defined inclusively as any quadrilateral with at least one pair of parallel sides. The latter definition is hierarchical, allowing the parallelogram, rhombus, and square to be included as its special case. In the case of an isosceles trapezoid, it is an acute trapezoid wherein two adjacent angles are acute on its longer base. Both rectangles and squares are usually considered to be special cases of isosceles trapezoids, whereas parallelograms are not. Another special case is a trilateral trapezoid or a trisosceles trapezoid, where two legs and one base have equal lengths; it can be considered as the dissection of a regular pentagon.

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 crossed isosceles trapezoids (crossed quadrilaterals in which the crossed sides are of equal length and the other sides are parallel) and 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 (or either pair of opposite sides in the case of a rectangle) of an isosceles trapezoid.

If a quadrilateral is known to be a trapezoid, it is not sufficient just to check that the legs have the same length in order to know that it is an isosceles trapezoid, since a rhombus is a special case of a trapezoid with legs of equal length, but is not an isosceles trapezoid as it lacks a line of symmetry through the midpoints of opposite sides.

Any one of the following properties distinguishes an isosceles trapezoid from other trapezoids:

In an isosceles trapezoid, the base angles have the same measure pairwise. In the picture below, angles ∠ABC and ∠DCB are obtuse angles of the same measure, while angles ∠BAD and ∠CDA are acute angles, also of the same measure.

Since the lines AD and BC are parallel, angles adjacent to opposite bases are supplementary, that is, angles ∠ABC + ∠BAD = 180°.

The diagonals of an isosceles trapezoid have the same length; that is, every isosceles trapezoid is an equidiagonal quadrilateral. Moreover, the diagonals divide each other in the same proportions. As pictured, the diagonals AC and BD have the same length (AC = BD) and divide each other into segments of the same length (AE = DE and BE = CE).