The Regular Hexagon
Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 53 of 61.
The side of a regular hexagon drawn in a circle equals the circle's radius. So the radius itself steps round the circle, exactly six times.
Why six? The circle about a corner V through the center O has the same radius as the big circle. Where it crosses the big circle, the point is a radius from O and a radius from V, so it makes an equilateral triangle with O and V, and the angle at O is 60°. Six angles of 60° make the full 360° around O, so six steps close up exactly.
On the board: a circle about A through O gives the two corners next to A. The line AO crosses the circle again at the corner opposite A, and a circle about that corner through O gives the last two. Mark all six corners with Point.
Challenge
Construct a regular hexagon in the circle: mark its six corners on the circle, one of them at A, then press Check.
Try it yourself
Construct it with a compass and straightedge
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Transformations & Constructions
7Drawing on Squared Paper
Lengths by PythagorasPerpendicular StepsSquares by AreaRight Triangles by AreaMidpoints on the GridRecap: Squared Paper10Perpendiculars and Parallels
Perpendicular From a PointPerpendicular at a PointParallel Through a PointTools You Have EarnedRecap: Parallels5Dilations
Scaling From a CenterShrinking a ShapeDilating About a PointNegative Scale FactorsRecap: Dilations8Compass and Straightedge
Circles Keep DistancesWhy the Sides MatchAngles You BuiltA 60° AngleRecap: Equilateral Triangle11Constructed Shapes
A Square on a SegmentThe Regular HexagonCopy an AngleA Tangent From a PointRecap: Constructed Shapes