A Construction
of a Rectangle
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 rectangle
is an equiangular 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.
- 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 the perpendicular line to segment
AB that passes through point B and use the Point on Object construction.
- Select point C and line BC and construct
a perpendicular line.
- Construct the intersection point of the two
lines.
- Construct the segments BC, CD, and DA.
- Select and hide the original lines.
- Click and drag any vertex and/or side to
make sure that your construction always holds true for the definition
of a rectangle.
- Using the selection tool, click and drag
around your constructed rectangle, so that the entire rectangle
is selected. Use the work menu to create
a script.
Using only the definition of a rectangle, what
measurement of the sides of a rectangle must be used to support
the claim that your construction is of a rectangle?
Extension:
Find another way to construct a rectangle.
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.