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Quadrilateral Summary Ways to show that a quadrilateral is a parallelogram If both pairs of opposite sides are parallel, then the quadrilateral is a parallelogram. If both pairs of opposite sides are congruent, then the quadrilateral is a parallelogram. If both pairs of opposite angles are congruent, then the quadrilateral is a parallelogram. If one pair of opposite sides is both parallel and congruent, then the quadrilateral is a parallelogram. If the diagonals bisect each other, then the quadrilateral is a parallelogram. Ways to show that a quadrilateral is a rectangle. If a quadrilateral has four right angles, then it is a rectangle. If a parallelogram has one right angle, then it is a rectangle. If a parallelogram has congruent diagonals, then it is a rectangle. Ways to show that a quadrilateral is a rhombus. If a quadrilateral has four congruent sides, then it is a rhombus. If a parallelogram has two consecutive sides congruent, then it is a rhombus. If a parallelogram has perpendicular diagonals, then it is a rhombus. Ways to show that a quadrilateral is a square. If a quadrilateral is both a rectangle and a rhombus, then it is a square. If a quadrilateral has four right angles and four congruent sides, then it is a square. Ways to show that a quadrilateral is a trapezoid. If a quadrilateral has exactly one pair of parallel sides, then it is a trapezoid. Ways to show that a quadrilateral is an isosceles trapezoid. If a quadrilateral has one pair of opposite sides parallel and the other pair of opposite sides congruent, then it is an isosceles trapezoid. If a trapezoid has congruent legs, then it is an isosceles trapezoid. If a trapezoid has congruent diagonals, then it is an isosceles trapezoid. Ways to show that a quadrilateral is a kite. If a quadrilateral has two pairs of adjacent sides congruent and no opposite sides congruent.