# My quadrilateral has congruent diagonals. What must it be?

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It could be an isosceles trapezoid, a rectangle, or a square.

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If a trapezoid has congruent diagonals, it is an isosceles trapezoid. A trapezoid is a quadrilateral with *one and only one pair of parallel sides.*

If a parallelogram, which has *two pairs of parallel sides* also has congruent diagonals, it is a rectangle.

A square is a special type of rectangle in which all sides are congruent, thus it follows the same properties, and has congruent diagonals.

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Your quadrilateral must be an isosceles trapezoid.

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Note that rectangles and squares also always have congruent diagonals, but an isosceles trapezoid is the most general term for all the possibilities, since rectangles and squares are isosceles trapezoids in addition to having their own unique properties.

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