Skill: Identify regular and irregular polygons

A polygon is a closed shape made of at least three straight sides. To decide whether it is regular, check two things:

1. Are all the side lengths equal?
2. Are all the interior angles equal?

• If both answers are yes, the polygon is regular.
• If either answer is no, it is irregular.

The shape’s color, size, or direction does not matter.

Example: A pentagon has side lengths

$$4\text{ cm},\ 4\text{ cm},\ 4\text{ cm},\ 4\text{ cm},\ 4\text{ cm}$$

and each interior angle measures $108^\circ$.

Step 1: Check the sides.
All five sides are $4$ cm, so the side lengths are equal.

Step 2: Check the angles.
All five angles measure $108^\circ$, so the angle measures are equal.

Step 3: Classify the polygon.
Both conditions are true, so the pentagon is a regular polygon.

If even one side had a different length or one angle had a different measure, the pentagon would be irregular.