Question

what statement proves a quadrilateral is a square?
quadrilateral abcd is a rhombus and a rectangle
quadrilateral abcd has diagonals that are either congruent or perpendicular bisectors
quadrilateral abcd is a trapezoid and a kite
quadrilateral abcd has 2 congruent sides and 2 congruent angles

Explanation:

• A rhombus has all sides equal and opposite sides parallel. A rectangle has all angles equal to \(90^{\circ}\) and opposite sides equal and parallel. A square has all the properties of a rhombus (all - side equal) and a rectangle (all angles \(90^{\circ}\)).
• For the second option: If diagonals are congruent, the quadrilateral could be a rectangle or an isosceles trapezoid. If diagonals are perpendicular bisectors, the quadrilateral could be a rhombus.
• A trapezoid has one pair of parallel sides and a kite has two pairs of adjacent equal sides. A square is not a trapezoid (as it has two pairs of parallel sides) and not a kite (as all sides are equal, not just adjacent pairs).
• A quadrilateral with 2 congruent sides and 2 congruent angles is too general and does not specifically define a square.

Answer:

Quadrilateral \(ABCD\) is a rhombus and a rectangle.