n Learning and Teaching Mathematics - Exploring the minimum conditions for congruency of polygons

Volume 2016, Issue 21
  • ISSN : 1990-6811


Polygons form an important component of Euclidean geometry within most school curricula. In the earliest grades pupils observe, describe and sort polygons according to their general characteristics. This then develops into a more sophisticated classification system based on properties and definitions in which various 'families' of polygons emerge. The general idea of congruency is then introduced, and is formally explored with a specific focus on triangles.

The formal exploration of congruency in polygons with more than three sides is seldom dealt with at school level. It is our contention that exploring congruency in polygons other than triangles is likely to enhance a more meaningful appreciation for the concept of congruency, and may prevent pupils from making erroneous generalisations. By way of example, pupils are familiar with the idea that two triangles are congruent when their sides are correspondingly equal. Pupils might thus fall prey to the misconception that two quadrilaterals are also congruent if their sides are correspondingly equal.
The purpose of this article is to present an exploration of congruency in polygons other than triangles. We first explore the necessary conditions to establish congruency in quadrilaterals, and then use an inductive process to establish a broader generalisation of congruency in polygons. It is hoped that such an exploration in the classroom will deepen pupilsâ?? appreciation for the concept of congruency.

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