6.3 Conditions for Parallelograms

Front

What is a parallelogram?

Back

A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

Front

State the conditions that prove a quadrilateral is a parallelogram.

Back

1. Both pairs of opposite sides are congruent. 2. Both pairs of opposite angles are congruent. 3. The diagonals bisect each other. 4. One pair of opposite sides is both parallel and congruent. 5. The sum of the interior angles is 360 degrees.

Front

How many theorems are there that prove if a quadrilateral is a parallelogram?

Back

There are 5 theorems.

Front

If a quadrilateral has two pairs of opposite sides that are congruent, what can we conclude?

Back

The quadrilateral is a parallelogram.

Front

What can be concluded if both pairs of opposite angles in a quadrilateral are congruent?

Back

The quadrilateral is a parallelogram.

Front

If the diagonals of a quadrilateral bisect each other, what can we conclude?

Back

The quadrilateral is a parallelogram.

Front

What does it mean for a quadrilateral to have one pair of opposite sides that are both parallel and congruent?

Back

It means the quadrilateral is a parallelogram.

Front

Can a quadrilateral be a parallelogram if only one pair of opposite sides is parallel?

Back

No, it must have both pairs of opposite sides parallel.

Front

What is the sum of the interior angles of a quadrilateral?

Back

The sum of the interior angles of a quadrilateral is 360 degrees.

Front

If a quadrilateral has two consecutive angles that are supplementary, what can we conclude?

Back

The quadrilateral is a parallelogram.