How To Prove a Parallelogram?
17 Step-by-Step Examples For Mastery!

In today’s geometry lesson, you’re going to learn the 6 ways to prove a parallelogram.

More specifically, how do we prove a quadrilateral is a parallelogram?

Finally, you’ll learn how to complete the associated 2 column-proofs.

Let’s jump in!

Well, we must show one of the six basic properties of parallelograms to be true!

1. Both pairs of opposite sides are parallel
2. Both pairs of opposite sides are congruent
3. Both pairs of opposite angles are congruent
4. Diagonals bisect each other
5. One angle is supplementary to both consecutive angles (same-side interior)
6. One pair of opposite sides are congruent AND parallel

So we’re going to put on our thinking caps, and use our detective skills, as we set out to prove (show) that a quadrilateral is a parallelogram.

This means we are looking for whether or not both pairs of opposite sides of a quadrilateral are congruent. Because if they are then the figure is a parallelogram.

In addition, we may determine that both pairs of opposite sides are parallel, and once again, we have shown the quadrilateral to be a parallelogram.

Another approach might involve showing that the opposite angles of a quadrilateral are congruent or that the consecutive angles of a quadrilateral are supplementary. Both of these facts allow us to prove that the figure is indeed a parallelogram.

We might find that the information provided will indicate that the diagonals of the quadrilateral bisect each other. If so, then the figure is a parallelogram.

A tip from Math Bits says, if we can show that one set of opposite sides are both parallel and congruent, which in turn indicates that the polygon is a parallelogram, this will save time when working a proof.

In the video below:

1. We will use the properties of parallelograms to determine if we have enough information to prove a given quadrilateral is a parallelogram.
2. Find missing values of a given parallelogram.
3. Write several two-column proofs (step-by-step).

Proving Parallelograms – Lesson & Examples (Video)

26 min

• Introduction to Proving Parallelograms
• 00:00:24 – How to prove a quadrilateral is a parallelogram? (Examples #1-6)
• Exclusive Content for Member’s Only

• 00:09:14 – Decide if you are given enough information to prove that the quadrilateral is a parallelogram. (Examples #7-13)
• 00:15:24 – Find the value of x in the parallelogram. (Examples #14-15)
• 00:18:36 – Complete the two-column proof. (Examples #16-17)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions