6-2 Properties of Parallelograms

What is a parallelogram?

Quadrilateral with both pairs of opposite sides parallel (PROPERTY #1).

In a quadrilateral, opposite sides do not share a vertex and opposite angles do not share a side.

If a quadrilateral is a parallelogram, then its opposite sides are congruent.

If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

m∠A + m∠B = 180° m∠A + m∠D = 180°
m∠D + m∠C = 180° m∠C + m∠B = 180°

Theorem 6-4 (PROPERTY #3)

• Angles of a polygon that share a side

What are they?

If a quadrilateral is a parallelogram, then its opposite anlges are congruent.

1. Opposite sides are parallel (2 sets)

2. Opposite sides are congruent (2 sets)

3. Consecutive angles are supplementary

4. Opposite angles are congruent (2 sets)

If a quadrilateral is a parallelogram, then its diagonals bisect each other.