L3 · Regular and irregular polygons

Learning goal

“I can classify a polygon as regular or irregular. A regular polygon has ALL sides equal AND ALL angles equal - I check both, every time.”

Regular polygon — a polygon whose sides are all equal AND whose angles are all equal, like a square or a stop-sign octagon.

Irregular polygon — a polygon that fails at least one of those tests: some sides differ, or some angles differ (or both).

Equal sides — (from L1) sides with exactly the same length, checked against each other.

Equal angles — (from L2) angles with exactly the same opening, checked against each other or against a shared referent.

Worked example

Classify two shapes. Shape 1 - a square: Side test: all 4 sides equal. Angle test: all 4 angles are right angles, so all equal. BOTH tests pass -> the square is a regular quadrilateral. Shape 2 - a triangle with every side 6 cm and every angle the same opening: side test passes, angle test passes -> regular triangle. Say it plainly: regular is a two-key lock. One key is equal sides. The other key is equal angles. The lock opens only when both keys turn.

Check yourself — explain it

A rectangle (not a square) passes the angle test - all 4 angles are equal right angles. Why is it still irregular?

Paired problem — example still visible

A pentagon has all 5 sides 4 cm long and all 5 angles equal. Regular or irregular? -> Regular (both tests pass)

Faded completion — last step is yours

"A shape has all sides equal, but one angle is bigger than the others. It fails the angle test, so it is ___." -> irregular

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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