Identifying similar triangles

This lesson develops the concept of identifying similar triangles. In particular students will:

• Use facts about the angle sum and exterior angles of triangles to calculate missing angles
• Apply angle theorems to parallel lines cut by a transversal
• Interpret geometrical diagrams using mathematical properties to identify similarity of triangles

The lesson begins with students working out angles on a diagram that shows parallel lines cut by a transversal. The diagram shows two triangles, the transversals that are not part of a common side can’t be assumed to be parallel. Where angles cannot be calculated, students must state why.

There are then eight cards featuring pairs of triangles. Students must decide whether or not the two triangles are similar, not similar, or if it can’t be determined. Reasons must be given for choices.

There are pre-lesson and post-lesson formative assessment tasks. Detailed teacher notes give suggestions on questioning and how to use the resources. Full solutions are given for each of the sections.

This is a concept development lesson from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. Further information on the collection is given here.