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.
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.
Return to
the Table of Contents.