Q: If a quadrilateral has four congruent sides and its diagonals are congruent?

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A quadrilateral with four congruent sides and uncongruent diagonals is a Rhombus. See related link for a picture

Rhombus.

Square.

square

A rhombus

A square would fit the given description.

trapezoid * * * * * It cannot be a trapezoid because that does not have four congruent sides. In fact it need not have even two congruent sides. The correct answer is a rhombus.

Two pairs of equal sides and four right angles.

A rectangle is a quadrilateral with four sides. All angles are right angles, the diagonals are congruent, and the opposite sides are all equal. A rhombus (diamond) is a quadrilateral with congruent daigonals and equal angles.

Square

Yes. A rhombus has four sides, qualifying it as a quadrilateral. Rhombuses also have four congruent (equal) sides.

An impossibility. By definition a quadrilateral with 4 congruent sides must have congruent adjacent angles.