Which description defines an isosceles trapezoid?

Which description defines an isosceles trapezoid?

• A. A trapezoid with all sides equal
• B. A trapezoid with two pairs of parallel sides
• C. A trapezoid whose nonparallel sides are congruent
• D. A trapezoid with diagonals perpendicular

Answer: (C)

An isosceles trapezoid has one pair of parallel sides (the bases) and the other two sides (the legs) equal in length. That equality of the nonparallel sides gives a symmetric shape, which also leads to equal base angles and equal diagonals. So the description that defines an isosceles trapezoid is a trapezoid whose nonparallel sides are congruent. The other descriptions describe different shapes: a trapezoid with all sides equal would be a different figure, two pairs of parallel sides would make a parallelogram, and diagonals perpendicular points to another special case not specific to isosceles trapezoids.

An isosceles trapezoid has one pair of parallel sides (the bases) and the other two sides (the legs) equal in length. That equality of the nonparallel sides gives a symmetric shape, which also leads to equal base angles and equal diagonals.

So the description that defines an isosceles trapezoid is a trapezoid whose nonparallel sides are congruent. The other descriptions describe different shapes: a trapezoid with all sides equal would be a different figure, two pairs of parallel sides would make a parallelogram, and diagonals perpendicular points to another special case not specific to isosceles trapezoids.