Question

what statement proves a quadrilateral is a square?

• quadrilateral abcd is a trapezoid and a parallelogram.
• quadrilateral abcd has 4 congruent sides and 4 congruent angles.
• quadrilateral abcd has diagonals that are either congruent or perpendicular bisectors.
• quadrilateral abcd is a trapezoid and a kite.

Explanation:

A square is defined as a quadrilateral with 4 congruent sides and 4 congruent right angles. Checking each option:

• A trapezoid and parallelogram overlap only if it's a parallelogram (trapezoid needs 1 pair of parallel sides, parallelogram has 2, but this doesn't prove a square).
• 4 congruent sides and 4 congruent angles directly matches the square definition.
• Diagonals being either congruent or perpendicular bisectors isn't sufficient (rectangles have congruent diagonals, rhombuses have perpendicular bisectors, but not necessarily both).
• A trapezoid and kite can't coexist (kite has 2 pairs of adjacent congruent sides, trapezoid has 1 pair of parallel sides—this combination doesn't form a square).

Answer:

B. Quadrilateral ABCD has 4 congruent sides and 4 congruent angles.