by David Wise

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

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

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.
- Construct line AD.
- 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**.

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the Table of Contents.