PROPERTIES AND DEFINITION OF QUADRILATERALS

• A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.
• A rectangle is a parallelogram with four right angles
• A rhombus is a parallelogram with four congruent sides.
• A square is a parallelogram with four right angles and four congruent sides.
• A trapezoid is a quadrilateral with exactly one pair of parallel sides.
• An isosceles trapezoid is a trapezoid with congruent legs.
• The median of a trapezoid is the segment joining the midpoints of the legs.
• A kite is a quadrilateral with two distinct pairs of congruent and adjacent sides.
• A diagonal of a parallelogram forms two congruent triangles.
• In a parallelogram, any two opposite angles are congruent.
•  In a parallelogram, any two consecutive angles are supplementary.
• In a parallelogram, any two opposite sides are congruent.
• The diagonals of a parallelogram bisect each other.
• The diagonals of a rectangle are congruent.
•  The diagonals of a square bisect the opposite angles.
•  The diagonals of a rhombus are perpendicular.
• Each diagonal of a rhombus bisects the opposite angles.
•  If a parallelogram has at least one right angle, then it is a rectangle.
• If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
• If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
• If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.
• If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
•  If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
• The segment that joins the midpoint of two sides of a triangle is parallel to the third side and is one-half of its measure.
• The base angles of an isosceles trapezoid are congruent.
• The diagonals of an isosceles trapezoid are congruent.
•  If the base angles of a trapezoid are congruent, then the trapezoid is isosceles.
• If the diagonals of a trapezoid are congruent, the trapezoid is isosceles.
• The median of a trapezoid is parallel to its bases.
• The median of a trapezoid is half the sum of the lengths of the bases.
• If exactly one diagonal of a quadrilateral is the perpendicular bisector of the other diagonal, then the quadrilateral is a kite.
• If a quadrilateral is a kite, then its diagonals are perpendicular.
• The area of a kite is half the product of the lengths of its diagonals.