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. |
About Angles | * If a quadrilateral is a parallelogram, the opposite angles are congruent. * If a quadrilateral is a parallelogram, the consecutive angles are supplementary. |
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 quadrilateral are parallel, the quadrilateral is a parallelogram. * If both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram. |
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. |
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. |