Properties of Parallelograms
Detailed w/ 21 Step-by-Step Examples!

Did you know that there are 6 distinct properties of parallelograms?

It’s true!

In today’s geometry lesson we’re going to learn to use those properties to uncover missing sides and angles from known parallelograms.

Then we’re going to dive into the associated two-column proofs!

Let’s get started!

A parallelogram is a special type of quadrilateral.

And just as its name suggests, a parallelogram is a figure with two pairs of opposite sides that are parallel.

But there are even more attributes of parallelograms that enable us to determine angle and side relationships.

Properties of Parallelograms Explained

1. Opposite sides are parallel

Segment AB is parallel to segment DC, and segment AD is parallel to segment BC.

2. Opposite sides are congruent

Segment AB is congruent to segment DC, and segment AD is congruent to segment BC.

3. Opposite angles are congruent

Angle A is congruent to angle C, and angle D is congruent to angle B.

4. Same-Side interior angles (consecutive angles) are supplementary

Angles A and D are supplementary, angles B and C are supplementary, angles A and B are supplementary, and angles D and C are supplementary.

5. Each diagonal of a parallelogram separates it into two congruent triangles

Triangle DAB is congruent to triangle DCB.

6. The diagonals of a parallelogram bisect each other

Segment AE is congruent to segment CE, and segment DE is congruent to segment BE.

And as Math Planet accurately points out, if one angle in a parallelogram is a right angle, then all angles are right angles.

This means that if we know the properties of parallelograms we can identify missing angles and sides.

We will be reminded of our angle pair relationships from our previous study of parallel lines cut by a transversal to aid us on our quest. Remember, all those rules for alternate interior angles, corresponding angles, and even vertical angles? They are going to come in handy!

And what we will discover is that if we have congruent polygons, then corresponding angles and sides are also congruent. This fact enables us to prove two parallelograms are congruent, all while using our properties.

Cool!

In the video below:

1. We will use our new properties of parallelograms to find unknown measures.
2. Prove corresponding parts of congruent parallelograms are congruent.

Parallelogram Properties – Lesson & Examples (Video)

32 min

• Introduction to Parallelograms
• 00:00:23 – Complete the missing statements for the given parallelogram (Examples #1-8)
• Exclusive Content for Member’s Only

• 00:08:56 – Use properties of parallelograms to find the missing side and angle measurements (Examples #9-18)
• 00:17:34 – Use the parallelogram properties to find the indicated measures (Example #19)
• 00:20:47 – Complete the two-column proof for the given parallelograms (Examples #20-21)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions