Quadrilateral Properties: Parallelogram

Before you start

What is a parallelogram?

Move points B and D and observe what happens to the parallelogram.

Parallelogram

In a quadrilateral, opposite sides are those across from each other, not touching or sharing any vertices. For example, AB and DC are opposite sides in the parallelogram here.

#1

Is there a relationship between opposite sides of the parallelogram? If so, what is the relationship?

Consecutive sides are those right next to each other (touching) in a polygon. For example, AB and BC are consecutive sides in this parallelogram.

#2

Is there a relationship between consecutive sides of the parallelogram? If so what is the relationship?

Now consider the angles in the diagram. Use the checkboxes as needed.

#3

What is the relationship between opposite angles of the parallelogram?

#4

What is the relationship between consecutive angles of the parallelogram?

Now let's add the diagonals to the parallelogram. Diagonals are segments that connect one vertex to another non-consecutive vertex.

#5

Are the diagonals of the parallelogram always congruent? How do you know?

#6

Do the diagonals of the parallelogram always bisect each other? How do you know?

#7

Are the two diagonals always perpendicular? How do you know?

#8

Do the diagonals always bisect the angles at the vertices? How do you know?