A Construction of a Rhombus
by David Wise

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

Definition: A rhombus is an equilateral parallelogram.

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

• Construct two points, A and B.
• Construct line AB.
• Select points A and B (point A first) and use Circle by Center and Point construction to construct a circle with center A
• Select the circle and use Point on Object construction to construct a point on the circle. Relabel the point D.
• Select point D and line AB and construct a parallel line to line AB.
• Select point B and line AD and construct a parallel line to line AD.
• Construct the intersection point of the two lines. Relabel the point C.
• Construct the segments AB, BC, CD, DA.
• Select and hide the original lines and circle.
• Click and drag any vertex and/or side to make sure that your construction always holds true for the definition of a rhombus.
• Using the selection tool, click and drag around your constructed rhombus, so that the entire rhombus is selected. Use the work menu to create a script.

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

Extension:
Find another way to construct a rhombus.

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.