Prove a Quadrilateral is a Parallelogram (7.3)

Front

What is a parallelogram?

Back

A parallelogram is a quadrilateral with opposite sides that are both parallel and congruent.

Front

What is the Parallelogram Opposite Sides Converse Theorem?

Back

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Front

What is the Parallelogram Opposite Angles Converse Theorem?

Back

If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Front

What is the Opposite Sides Parallel and Congruent Theorem?

Back

If one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram.

Front

What is the Parallelogram Diagonals Converse Theorem?

Back

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

Front

Is a quadrilateral with one pair of opposite sides parallel and congruent a parallelogram?

Back

Yes, it is a parallelogram.

Front

What information is needed to prove a quadrilateral is a parallelogram?

Back

You need to show that either both pairs of opposite sides are congruent, both pairs of opposite angles are congruent, or that the diagonals bisect each other.

Front

If two pairs of consecutive sides of a quadrilateral are congruent, is it a parallelogram?

Back

No, there is not enough information to conclude it is a parallelogram.

Front

What can be concluded if one pair of opposite sides of a quadrilateral is parallel?

Back

It cannot be concluded that the quadrilateral is a parallelogram unless the other pair of opposite sides is also parallel.

Front

What does it mean for diagonals to bisect each other?

Back

It means that each diagonal divides the other into two equal parts.