Explorations on given polygons extend a student's concept of both the properties of such polygons and the applications of using those properties. Above appears to be one simple example that when extended with investigation broadens the conceptualization of Geometric Proof and Algebraic Reasoning.

First, I will explain the **GIVEN
CHARACTERISTICS** of the square ABCD. Then, I will provide
a **PROOF** that the inside
quadrilateral is a square. Finally, I will extend my investigation
so as to give an **ALGEBRAIC EXPLANATION**
of the limits of the inside square.