a four-sided figure which has two opposite sides of the same length, and the shape is vertically symmetrical

a quadrilateral with one pair of parallel sides and congruent base angles, or it is a trapezoid with congruent base angles

a trapezoid in which the base angles are equal so

a trapezoid with the two non-parallel sides the same length

A trapezoid in which the two nonparallel sides are congruent.

A trapezoid with congruent legs.

A trapezoid whose two nonparallel sides are the same length (Lesson 6.3).

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. Also, an isosceles trapezoid's base angles are congruent.