#7.3 Proving that a Quadrilateral is a Parallelogram

Front

What is the Opposite Sides Parallel and Congruent Theorem?

Back

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

Tags

CCSS.HSG.CO.C.11

Front

What is the Parallelogram Diagonals Converse Theorem?

Back

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

Tags

CCSS.HSG.CO.C.11

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.

Tags

CCSS.HSG.CO.C.11

Front

What is a parallelogram?

Back

A parallelogram is a quadrilateral with opposite sides that are both parallel and equal in length.

Tags

CCSS.3.G.A.1

Front

How can you prove a quadrilateral is a parallelogram using opposite sides?

Back

Show that both pairs of opposite sides are equal in length or parallel.

Tags

CCSS.HSG.C.A.3

Front

How can you prove a quadrilateral is a parallelogram using angles?

Back

Show that both pairs of opposite angles are equal.

Tags

CCSS.HSG.C.A.3

Front

How can you prove a quadrilateral is a parallelogram using diagonals?

Back

Show that the diagonals bisect each other.

Tags

CCSS.HSG.CO.C.11

Front

If one pair of opposite sides of a quadrilateral is both parallel and congruent, what can be concluded?

Back

The quadrilateral is a parallelogram.

Front

What is the relationship between the angles in a parallelogram?

Back

The opposite angles are equal, and the consecutive angles are supplementary.

Tags

CCSS.HSG.C.A.3

Front

If a quadrilateral has one pair of opposite sides that are parallel, what additional condition must be met for it to be a parallelogram?

Back

The other pair of opposite sides must also be parallel.