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 Quadrilateral A four-sided polygon. Parallelogram A quadrilateral with both pairs of opposite sides parallel. If a quadrilateral is a parallelogram, then both pairs of opposite sides are... congruent and parallel. If a quadrilateral is a parallelogram, then both pairs of opposite angles are... congruent. If a quadrilateral is a parallelogram, then its diagonals... bisect each other. If a quadrilateral is a parallelogram, then its consecutive angles are... supplementary. Parallelogram Opposite Sides Theorem: Opposite sides of a parallelogram are congruent. Parallelogram Opposite Angles Theorem: Opposite angles of a parallelogram are congruent. Parallelogram Consecutive Angles Theorem: Consecutive angles of a parallelogram are supplementary. Parallelogram Diagonals Theorem: The diagonals of a parallelogram bisect each other. Quadrilateral Parallel and Congruent Sides Theorem: If one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram. Converse of the Quadrilateral Opposite Sides Theorem: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Converse of the Quadrilateral Opposite Angles Theorem: If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Converse of the Quadrilateral Diagonals Theorem: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. Opposite, Parallel, Congruent Theorem: If one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram. Rectangle Theorem: If a parallelogram is a rectangle, then its diagonals are congruent. Converse of the Rectangle Theorem: If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. If a quadrilateral is a rectangle, then opposite sides are ___________ and _____________. congruent and parallel If a quadrilateral is a rectangle, then opposite angles are ____________. congruent If a quadrilateral is a rectangle, then consecutive angles are ___________. supplementary If a quadrilateral is a rectangle, then diagonals are ______________ and ______________ each other congruent and bisect If a quadrilateral is a rectangle, then all four angles are ___________. right (90 degrees) Rhombus Diagonal Theorem: The diagonals of a rhombus are perpendicular. Converse of the Rhombus Diagonal Theorem: If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. Rhombus Angle Bisector Theorem: Each diagonal of a rhombus bisects a pair of opposite angles. If a quadrilateral is both a rhombus and a rectangle, it is a ____________. square Isosceles Trapezoid Base Angles Theorem: Both pairs of base angles of an isosceles trapezoid are congruent. Isosceles Trapezoid Diagonal Theorem: The diagonals of an isosceles trapezoid are congruent. Trapezoid Median Theorem: The median of a trapezoid is parallel to the bases, and its measure is one-half the sum of the measures of the bases.