Four Parallelogram Properties
In this investigation you will discover some special properties of parallelograms. A parallelogram is a quadrilateral whose opposite sides are parallel.
Sides of a Parallelogram
First lets look at opposite sides of a parallelogram. Drag the slider. What do you notice? Adjust the pink vertices to see if this is true for every parallelogram (any size/shape). Complete the conjecture below.
Parallelogram Opposite Sides Conjecture
The opposite sides of a parallelogram are _____.
Interior Angles of a Parallelogram
Use the applet above to interact with the angles in a parallelogram. First, look at the opposite angles, or the angles that are across from each other. What do you notice about opposite angles? Move the pink vertices to see if this is true for ALL parallelograms. Then, complete the conjecture below.
Parallelogram Opposite Angles Conjecture
The opposite angles of a parallelogram are _____.
Interior Angles of a Parallelogram (2)
Two angles that share a common side are called consecutive angles. As you interact with the applet, notice the top left vertex of the parallelogram. What do you think the sum of consecutive angles is? (In other words, what is the blue angle plus the pink angle?)
Parallelogram Consecutive Angles Conjecture
The consecutive angles of a parallelogram are _____.
Diagonals of a Parallelogram
Finally, let's consider the diagonals of a parallelogram. What do you notice about the diagonals? Adjust the pink vertices to make sure this works for ALL parallelograms. Then, complete the conjecture below.
Parallelogram Diagonals Conjecture
The diagonals of a parallelogram _____.