Parallelogram Theorems

What is the definition of a parallelogram?

• A quadrilateral with two pairs of parallel sides.

• A quadrilateral with two pairs of congruent sides.

• A quadrilateral with two pairs of congruent angles.

• A quadrilateral with two pairs of congruent diagonals.

The Opposite Sides Theorem states that opposite sides of a parallelogram are:

• parallel

• congruent

• perpendicular

The Opposite Angles Theorem states that opposite angles of a parallelogram are:

• supplementary

• congruent

• complementary

The Consecutive Angles Theorem states that consecutive angles of a parallelogram are:

• supplementary

• congruent

• complementary

The Diagonals Theorem states that the diagonals of a parallelogram:

• are congruent

• bisect each other

• are parallel

• are perpendicular

The Opposite Sides Theorem states that a quadrilateral is a parallelogram if:

• both pairs of its opposite sides are parallel.

• both pairs of its opposite sides are congruent.

• both pairs of its opposite sides are perpendicular.

• one pair of its opposite sides are congruent.

• one pair of its opposite sides are parallel.

The Opposite Angles Theorem states that a quadrilateral is a parallelogram if:

• both pairs of its opposite angles are congruent.

• both pairs of its opposite angles are supplementary.

• one pair of its opposite angles are congruent.

• one pair of its opposite angles are supplementary.

The Consecutive Angles Theorem states that a quadrilateral is a parallelogram if:

• it has one angle that is supplementary to each of its consecutive angles.

• it has one angle that is congruent to each of its consecutive angles.

• it has two pairs of consecutive angles that are supplementary.

• it has two pairs of consecutive angles that are congruent.

The Diagonals Theorem states that a quadrilateral is a parallelogram if:

• its diagonals are congruent.

• its diagonals bisect each other.

• its diagonals are perpendicular.

• its diagonals are parallel.

The One Side Congruent and Parallel Theorem states that a quadrilateral is a parallelogram if it has __________ that are both congruent and parallel.

• one pair of opposite sides

• one pair of consecutive sides