Classifying polygons

First, student will learn how to identify triangles, quadrilaterals, pentagons, hexagons, etc. Here's practice. After that, students will learn what it means for a polygon to be equilateral or equiangular.

Next, students will see a proof that equilateral doesn't imply equiangular, and vice-versa. This is easily proven by counterexample. In the figure below, the pentagon on the left is equilateral but not equiangular, and the rectangle on the right is equiangular but not equilateral. Thus, equilateral doesn't imply equiangular, and vice-versa. There are infinitely many counterexamples, so you don't necessarily need to use the two I've provided.

After that, students will learn that polygons which are equilateral and equiangular are called regular. Any polygon which is not regular can be called irregular. What's commonly referred to as an equilateral triangle could also be characterized as a regular triangle, or the triangle which is both equilateral and equiangular. All of these phrases would refer to the same shape.

After that, students should learn the definition of concave and convex. Demonstrate that concave polygons can be equilateral but not equiangular. They cannot be equiangular because all concave polygons have at least one angle greater than \(180^\circ\) and at least one angle less than \(180^\circ.\) Students can practice classifying polygons here.