What is a parallelogram?
Let’s begin with defining some of the properties of a parallelogram.
1. A parallelogram is a four sided polygon.
2. The opposite sides of a parallelogram are parallel. So if you look at the picture below, sides AB and CD are parallel and AD and BC are parallel
3. The opposite angles of a parallelogram are congruent. So angles B and D are congruent and angles A and C are congruent. ( See picture above) For example if angle B is 120 degrees then angle D will also be 120 degrees. The same rule applies for angles D and B
4. The consecutive angles in a parallelogram are supplementary which means they add to 180 degrees. Therefore, if angle D measures 120 degrees, angle A will measure 60 degrees because they are consecutive angles and add up to 180 degrees.
5. In a parallelogram any two consecutive angles will be supplementary to each other. In the picture, A and B,B and C, C and D, and D and A are all consecutive angles and therefore, are supplementary.
Let’s look at a practice problem. Given a parallelogram in which angle C is has a measure of 80 degrees. What are the other three angles?