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.