Properties of a Parallelogram

• Definition: Quadrilateral with both pairs of opposite sides are parallel

  AB // DC , AD // BC

  
• Parallelogram Opposite Sides Theorem: If parallelogram, then opposite sides are congruent.

  AD is congruent to BC, AB is congruent to DC

  
• Parallelogram opposite angles theorem: If a parallelogram, then opposites angles are congruent.

  Angle A is congruent to angle C, angle B is congruent to angle D
• Parallelogram Consecutive Angles theorem: if a parallelogram, then consecutive angles are supplementary

  x+y = 180

  
• Parallelogram Diagonals theorem: If a parallelogram, diagonals bisect each other.

  BM is congruent to MD, AM is congruent to MC.
• Opposite sides Parallel and Congruent Theorem: If one pair of sides is parallel and congruent, then parallelogram