Math Tip of the Week: Learning Geometry by Working with GeoGebra

Geometry is one of the toughest subjects for many students, as indicated by the groans and eye-rolling you often see when asking them about their geometry class. A good tutor can help you become really comfortable with this subject, but a great complementary way to learn geometry is by using a software suite called GeoGebra. It can be downloaded here: http://www.geogebra.org/cms/en/

For example, suppose you would like confirmation the following statement is true:

If two chords intersect on the circumference of the circle to form perpendicular line segments, then the chord which connects their other endpoints must be a diameter of the circle.

Try using GeoGebra to confirm this. First draw circle A with perpendicular chords BC and CD (note, the angle can be constrained to be exactly 90 degrees but 89.97 degrees drawn freehand will be close enough!)

Now draw chord BD to connect their other endpoints and you will notice it passes right through the center of the circle at point A and thus BD is a diameter.

Therefore a right triangle is revealed, which should be the case since angle BCD should intercept an arc of twice its angular measure, or 180 degrees.

Ask your online tutor if you can use GeoGebra and work out some geometry problems together.