Describing and defining triangles

This lesson develops the concept of constructing triangles with given conditions. In particular students will:

• Recall and apply triangle properties
• Determine whether a set of given conditions for the measures of angle and/or sides of a triangle describe a unique triangle, more than one possible triangle or do not describe a possible triangle.

An introductory task presents a series of conditions and asks if it is possible to construct a triangle from them, and if so, is the triangle unique.

A collaborative activity develops the theme further. As an example, a card has the following conditions:

AB = 4 cm

AC = 4 cm

Angle B = 40˚

Students must decide if a triangle can be produced from these conditions. They must then decide if the triangle is unique or if further examples can be produced.

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.