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Looking beyond the lines

Visualising shapes that are embedded in diagrams can be difficult as students may be distracted by other lines. Colour (and transformations) can highlight the embedded shapes. This helps students visualise angle and length relationships.

You can download the Looking beyond the lines slide show presentation to use with your class. In this presentation, the required triangles are coloured and then translated out of the diagram. After separating them from within the more complex diagram, and marking equal angles, the similar triangles are more obvious.

The strategy of using colour to simplify the diagram is also very useful when exploring angle relationships in complex circle geometry problems. You can download the Linking angles slide show presentation which explains the process of working through a complex circle problem to use with your class.

Visualising relationships

In geometrical diagrams it can be difficult to recognise relationships. Strategies for analysing the diagrams and the use of dynamic representations can assist.