A Construction of a Rectangle
by David Wise

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

Definition: A rectangle is an equiangular parallelogram.

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

• Construct two points, A and B.
• Construct segment AB.
• Select point A and segment AB and construct a perpendicular line.
• Select point B and segment AB and construct a perpendicular line.
• Select the perpendicular line to segment AB that passes through point B and use the Point on Object construction.
• Select point C and line BC and construct a perpendicular line.
• Construct the intersection point of the two lines.
• Construct the segments BC, CD, and 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 rectangle.
• Using the selection tool, click and drag around your constructed rectangle, so that the entire rectangle is selected. Use the work menu to create a script.

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

Extension:
Find another way to construct a rectangle.

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.