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Resources - Secondary Mathematics

The ‘Describing and defining triangles’ resource is a concept development lesson from the ‘Mathematics Assessment Resource Service’ (MARS). The resource is intended to help students:

• Recall and apply triangle properties.
• Sketch and construct triangles with given conditions.
• 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.

The resource has a formative assessment task that students complete sometime before the lesson. The task explores how well students understand properties of triangles and constructing triangles from a given set of conditions.

The task presents students with information about triangle ABC and they must decide if:

• It is possible to construct a unique triangle ABC.
• It is possible to construct more than one triangle ABC.
• It is not possible to construct a triangle ABC with the given properties.

In each instance, reasoning must be given.

An example gives the following information: AB = 10 cm, BC = 11 cm, AC = 9 cm. From this information it is possible to construct a unique triangle ABC: In general, a unique triangle may always be drawn if three side lengths are given and the sum of any two is greater than the third.

A final task on the assessment considers triangle ABC which is isosceles with AB = 5 cm, and angle B = 48º. Triangle DEF is isosceles with DE = 5 cm and angle E = 48º. Students must explain why the two triangles might not be identical. The diagram below shows an explanation. The resource contains detailed guidance and suggested prompts for the common difficulties that students have had in completing this task.

The whole class introduction to the lesson makes use of the following slide: Suggested questions are:

• What facts do you know about triangles?
• What names do you know for different types of triangle?
• How do we label sides and angles if they are equal in magnitude?

It is recommended to encourage the class to give as much information as they can about the properties of a triangle and to check that they know how sides and angles may be labelled as equal in magnitude.

There is a small group collaborative task that follows a similar format to the introductory task. Students work with 10 cards showing properties and must determine if it is possible to use the description to construct a triangle, and if is, whether the triangle is unique or not.

There is a formative assessment task for students to complete sometime after the lesson. This shows how well they have grasped the concepts in the lesson.