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.
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.