Which description defines an isosceles trapezoid?

Which description defines an isosceles trapezoid?

• A. A trapezoid with all angles equal.
• B. A trapezoid whose nonparallel sides are congruent.
• C. A parallelogram with equal diagonals.
• D. A trapezoid with equal bases.

Answer: (B)

Isosceles trapezoid means a trapezoid with one pair of parallel sides and the other pair equal in length. That equality of the nonparallel sides (the legs) creates symmetry, which is why base angles are equal and diagonals are equal as well. So the defining description is that the nonparallel sides are congruent. The other ideas describe different shapes: a trapezoid with all angles equal would be a rectangle, a parallelogram with equal diagonals is also a rectangle, and a trapezoid with equal bases doesn’t necessarily make the legs equal.

Isosceles trapezoid means a trapezoid with one pair of parallel sides and the other pair equal in length. That equality of the nonparallel sides (the legs) creates symmetry, which is why base angles are equal and diagonals are equal as well. So the defining description is that the nonparallel sides are congruent. The other ideas describe different shapes: a trapezoid with all angles equal would be a rectangle, a parallelogram with equal diagonals is also a rectangle, and a trapezoid with equal bases doesn’t necessarily make the legs equal.