Discovering Some Properties of Parallelograms
by David Wise

Note: I recommend that this page be printed out, so that the instructions are easier to follow.

Definition: A parallelogram is a quadrilateral whose opposite sides are parallel.

• Use the measure menu to find the measure of each angle of the parrallelogram.
a. Remember to use the shift key when selecting more than one object.
b. Remember that the points must be selected a counterclockwise order to obtain a positive angle measure in directed degrees.
• Compare the measure of the opposite angles.
a. Click and drag any vertex.
b. Click and drag any side.
c. Does there appear to be a special relationship? If so, state it in the following conjecture.

C-52 The opposite angles of a parallelogram are___________________________________.

• Select a pair of consecutive angles and use the measure menu ---calculate--- to find the sum.
a. Repeat this process for all pairs of consecutive angles.
b. How many pairs of consecutive angles are there?
• Compare the measures of the sum of each pair of consecutive angles.
a. Click and drag any vertex.
b. Click and drag any side.
c. Does there appear to be a special relationship? If so, state it in the following conjecture.

C-53 The consecutive angles of a parallelogram are________________________________.

• Use the measure menu to find the measure of each side of the parallelogram.
a. How do you measure distance?
b. How do you measure length?
• Compare the measure of the opposite sides.
a. Click and drag any vertex.
b. Click and drag any side.
c. Does there appear to be a special relationship? If so, state it in the following conjecture.

C-54 The opposite sides of a parallelogram are____________________________________.

• Construct the two diagonals of the parallelogram.
• Construct the intersection point of the diagonals.
• Each diagonal is divided into two smaller segments. Use the measure menu to measure each of the four smaller segments. (Remember that depending upon how you want to measure each of these segments you may or may not have to construct the four smaller segments.)
• Compare the measure of the four smaller segments of the diagonals. Pay particular attention to each pair of smaller segments that make up each diagonal.
a. Click and drag any vertex.
b. Click and drag any side.
c. Does there appear to be a special relationship? If so, state it in the following conjecture.

C-55 The diagonals of a parallelogram are _____________________________of each other.

If you have any questions while trying to complete this investigation, or suggestions that would be useful, especially for use at the high school level, please send e-mail to esiwdivad@yahoo.com.