Classify polygons

Objective. Identify polygons from side, angle and symmetry properties.

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2. Worked example
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Learn: the key idea

A polygon is a closed two-dimensional shape made entirely of straight sides, classified by its number of sides, the equality of those sides and angles, and its symmetry. A regular polygon has all sides and all angles equal, such as a regular hexagon with six equal sides and six equal angles of 120° each, while an irregular polygon does not. Polygons are also named by their number of sides: a pentagon has 5 sides, a hexagon has 6, and an octagon has 8. Checking both side lengths and angle sizes together is needed to decide whether a polygon is regular.

Worked example

Classify a polygon with 7 equal sides and 7 equal angles, naming it fully.

1 $Count the number of sides: 7.$
2 $Recall that a 7-sided polygon is called a heptagon.$
3 $Check that all sides and all angles are equal.$
4 $Since both conditions hold, classify the polygon as regular.$

Answer: Regular heptagon

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Common mistake. Pupils sometimes assume a polygon is regular just because its sides look equal, without checking the angles are also equal. Always confirm both equal sides and equal angles before calling a polygon regular.

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