A Construction of a Parallelogram
Using Geometer's Sketchpad
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.

Click here to link to a new GSP sketch to complete a construction of a parallelogram.

When completing a construction, use the definition as a guide.

• Construct two points, A and B.
• Construct line AB.
• Construct point C, not on line AB.
• Construct line BC.
• Select point C and line AB and construct a parallel line to line AB.
• Select point A and line BC and construct a parallel line to line CB.
• Construct the intersection point of the two lines.
• Construct the segments AB, BC, CD, DA.
• Select and hide the original lines.
• Click and drag any vertex and/or side to make sure that your construction always holds true for the definition of a parallelogram.
• Using the selection tool, click and drag around your constructed parallelogram, so that the entire parallelogram is selected. Use the work menu to create a script.

Using only the definition of a parallelogram, what measurement of the sides of a parallelogram must be used to support the claim that your construction is of a parallelogram?

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.

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