A regular polygon is a closed plane figure with at least three straight sides in which all side lengths and all interior angles are equal; a polygon is irregular if either side lengths or angle measures are not all equal. Classification depends on these invariant attributes, not on orientation, color, or apparent size, and supports later reasoning about symmetry, perimeter, angle relationships, and area.
A polygon is a closed shape made of at least three straight sides. To decide whether it is regular, check two things:
The shape’s color, size, or direction does not matter.
Example: A pentagon has side lengths
and each interior angle measures .
Step 1: Check the sides.
All five sides are cm, so the side lengths are equal.
Step 2: Check the angles.
All five angles measure , 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.
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