Conserved properties in polygons obtained by a point reflecting process

ABSTRACT

The present paper describes a dynamic investigation of polygons obtained by reflecting an arbitrary point located inside or outside a given polygon through the midpoints of its sides. The activity was based on hypothesizing on the shape of the reflection polygon that would be obtained, testing the hypotheses using dynamic software, and finding a justified mathematical proof. The activity was also applied to properties that are conserved or not conserved as a result of the reflection. Additionally, we find the mathematical relation for the ratio between the area of the reflection polygon and the area of the original polygon. The population of the study was pre-service teachers and experienced teachers who study in teaching college.

KEYWORDS:

• Dynamic investigation of invariant (conserved) properties
• reflection in different polygons
• generalization of properties

Disclosure statement

No potential conflict of interest was reported by the authors.