and a Construction of a Square

by David Wise

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

Definition: A

__Special Properties__

Based upon the definitions of a square, a rectangle is a special type of rhombus and a special type of rectangle. This means that a square demonstates all of the same properties as a rhombus and rectangle. In addition, a rhombus and rectangle are both parallelograms, therefore, a square demonstrates all of the same properties as a parallelogram.

__Construction__

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

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 point A and segment AB and construct a circle by center and radius.
- Select the circle and the perpendicular line to segment AB and construct the point at intersection. Relabel the point D.
- Select point B and segment AB and construct a circle by center and radius.
- Select the circle and the perpendicular line to segment AB and construct the point at intersection. Relabel the point C.
- Construct the segments BC, CD, and DA.
- Select and hide the original lines, circles, and 2 extra intersection points.
- Click and drag any vertex and/or side to make sure that your construction always holds true for the definition of a square.
- Using the selection tool, click and drag around your constructed square, so that the entire square is selected. Use the work menu to create a script.

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

Extension:

Find another way to construct a square.

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.