P ROPERTIES OF P ARALLELOGRAMS Geometry CP1 (Holt 6-2)K.Santos

Q UADRILATERAL Quadrilateral—is a polygon with four sides

P ARALLELOGRAM

T HEOREM 6-2-1

T HEOREM 6-2-2

T HEOREM 6-2-3

E XAMPLE -- ANGLES

THEOREM 6-2-4

E XAMPLE —D IAGONALS Given the parallelogram below. Find w and z. 4z – 9 w + 8 3w 2z Diagonals of a parallelogram bisect each other. 3w = w + 82z = 4z - 9 2w = 8-2z = -9 w = 4z = 4.5

P ROPERTIES OF P ARALLELOGRAMS --both pairs of opposite sides are parallel --both pairs of opposite sides are congruent --both pairs of opposite angles are congruent --all pairs of consecutive angles are supplementary --both diagonals bisect each other

P ROOF

P ROOF : O PPOSITE SIDES OF A PARALLELOGRAM ARE CONGRUENT