2. Theorems that prove quadrilaterals to be parallelograms
• If both pairs of opposite sides are
congruent, it is a parallelogram
• If both pairs of opposite angles are
congruent, it is a parallelogram
• If an angle is supplementary to both of
its consecutive angles, it is a
parallelogram
• If the diagonals bisect each other, it is
a parallelogram
• If one pair of opposite sides are
congruent and parallel, it is a
parallelogram
3. Summary of properties that prove it a parallelogram
• Both pairs of opposite sides are
parallel
• Both pairs of opposite sides are
congruent
• Both pairs of opposite angles are
congruent
• One set of sides is congruent and
parallel
• Diagonals bisect each other
• One angle is supplementary to both
of its consecutive angles
