A Discussion of Some Special Properties
and a Construction of a Square

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 square is an equiangular rhombus.
Definition: A square is an equilateral rectangle.

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.


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.

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?

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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