Constructing Perpendicular Lines

In geometric construction we use Mathomat V7 as a tool to construct models.

What we draw is called a "figure" because it contains geometric relationships. These relationships are essential in design and construction. For example, if a builder is constructing a house which is shaped as a parallelogram, they need to measure its diagonals to make sure they are the same length.

Mathomat is a powerful tool for geometric construction. When using Mathomat the underlying geometric object you are working with, such as a parallelogram, is physically present in you hand as you draw. This makes it possible to think more creatively about the abstract geometric relationships in your figure as you work.

Mathomat has many different functions that can be used for geometric constructions. We explore these in the Mathomat Builder manual activities. This includes using Professor Tisdell's TGT in Mathomat to replace compass and straight edge construction with a more efficient, safer and more accurate alternative.

There are many reasons for doing geometric construction in school. These include deepening student understanding of basic geometry, and for proof and discovery of geometric properties using accurate drawings at more senior levels. Some of the teachers who use Mathomat in classrooms have given the following reasons for doing geometric construction:

• Making posters for the classroom. Teachers often insist on these being hand drawn. Drawing tools make accurate construction possible.
• At the start of the geometry topic to introduce spatial reasoning.
• As an underlying process for many different geometry topics, such as understanding protractors or working with symmetry.

This activity is from pages 35 and 36 of the Mathomat V7 Builder Manual.

1. Read the two activities in the instruction guide.
2. Print the activities as action sheets.
3. Follow steps one to six to draw perpendicular lines using the protractor in Mathomat V7.
4. Experiment with using the Arc builder scale in Mathomat V7 to do the same thing.

It is important to understand how to do geometric construction in many different ways. Constructing geometric figures involves thinking about the underlying mathematics of the drawing.