Quadrilaterals

Parallelograms - About Sides * If a quadrilateral is a parallelogram, the opposite sides are parallel. * If a quadrilateral is a parallelogram, the opposite sides are congruent. Parallelograms - About Angles * If a quadrilateral is a parallelogram, the opposite angles are congruent. * If a quadrilateral is a parallelogram, the consecutive angles are supplementary. Parallelograms - About Diagonals * If a quadrilateral is a parallelogram, the diagonals bisect each other. * If a quadrilateral is a parallelogram, the diagonals form two congruent triangles. Parallelogram Converses - About Sides * If both pairs of opposite sides of a quadrilatera are parallel, the quadrilateral is a parallelogram. * If both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram. Parallelogram Converses - About Angles * If both pairs of opposite angles of a quadrilateral are congruent, the quadrilateral is a parallelogram. * If the consecutive angles of a quadrilateral are supplementary, the quadrilateral is a parallelogram. Parallelogram Converses - About Diagonals * If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram. * If the diagonals of a quadrilateral form two congruent triangles, the quadrilateral is a parallelogram. Parallelogram If one pair of sides of a quadrilateral is BOTH parallel and congruent, the quadrilateral is a parallelogram. Rectangle If a parallelogram has one right angle it is a rectangle A parallelogram is a rectangle if and only if its diagonals are congruent. A rectangle is a parallelogram with four right angles. Rhombus A rhombus is a parallelogram with four congruent sides. If a parallelogram has two consecutive sides congruent, it is a rhombus. A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles. A parallelogram is a rhombus if and only if the diagonals are perpendicular. Square A square is a parallelogram with four congruent sides and four right angles. A quadrilateral is a square if and only if it is a rhombus and a rectangle. Trapezoid A trapezoid is a quadrilateral with exactly one pair of parallel sides. Isosceles Trapezoid An isosceles trapezoid is a trapezoid with congruent legs. A trapezoid is isosceles if and only if the base angles are congruent A trapezoid is isosceles if and only if the diagonals are congruent If a trapezoid is isosceles, the opposite angles are supplementary.