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Regular Polygons

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 28 of 61.

A regular polygon has all sides equal and all angles equal. A regular polygon with n sides has n lines of symmetry and rotational symmetry of order n.

$A regular pentagon with one of its five lines of symmetry$

For this regular pentagon, each line runs from a corner to the middle of the opposite side, one line for each corner: 5 lines. It matches every fifth of a turn, every 72°, so its order is 5. When n is even, the lines come in two kinds: half of them join opposite corners and half join the midpoints of opposite sides.

Challenge

ABCDEF is a regular hexagon. Draw every line of symmetry and give its order of rotational symmetry, then press Check.

Try it yourself

$Move the shape onto its target$

Move the shape onto its target

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Transformations & Constructions

1Translations

Sliding a Shape Draw the Image Image Coordinates The Translation Rule Recap: Translations

4Combining Moves

One Move, Then Another Order Matters Two Mirrors Name the Move Recap: Combining Moves

7Drawing on Squared Paper

Lengths by Pythagoras Perpendicular Steps Squares by Area Right Triangles by Area Midpoints on the Grid Recap: Squared Paper

10Perpendiculars and Parallels

Perpendicular From a Point Perpendicular at a Point Parallel Through a Point Tools You Have Earned Recap: Parallels

3Rotations

Turning About a Point The Half Turn Quarter-Turn Rules A Center Off the Origin Recap: Rotations

6Symmetry

Lines of Symmetry Rotational SymmetryRegular PolygonsSymmetry Is a Move Recap: Symmetry

9Bisectors

The Perpendicular Bisector The Midpoint Bisecting an Angle Half of 60°Recap: Bisectors

12Final Challenges

Final: Footprints Final: Two Moves, One Rule Final: Mirror on the Grid Final: The Fair Well Final: The Tangent Road