Build-Ups - Teacher’s Notes

Electronic (Dynamic geometry) versions

The essence of these activities is that images representing given facts are used to ‘build up’ new geometrical properties.

Each layer of the build-up contains a given fact to be shown on the diagram; for example, angles on a straight line add to 180°.

Mathematical conventions are introduced; for example, arrows are marked on parallel lines.

General definitions are also established. For example, alternate angles are defined by their positions relative to a transversal and a pair of non-parallel or parallel lines, as shown in the diagram.

Screen shot 2011-01-19 at 11.13.56

As the layers build up, given facts are recorded and these can then be used in subsequent build-ups.

There are three dynamic geometry files, each in versions for The Geometer’s Sketchpad, Cabri Géomètre and Geogebra.