Compass constructionsInscribe a regular polygon
Name: Date:
Inscribe each shape in its circle. Leave your arcs showing.
1Inscribe a square.
2Inscribe a square.
3Inscribe an equilateral triangle.
4Inscribe a regular hexagon.
Inscribe a regular polygon worksheets
The radius of a circle steps round it exactly six times. That single fact gives a regular hexagon, and joining every other mark gives an equilateral triangle — the square needs a different idea.
If they get stuck
Inscribe a regular polygon
The answer key prints on a separate page.
What's on this sheet
Keep the compass at the circle's radius and step it round from any point on the circle: you get six marks, evenly spaced, because six equilateral triangles fit round a center. Join all six for a hexagon, join every other one for an equilateral triangle. Nothing is measured and nothing is divided — the hexagon falls out of the radius itself.
Why this sheet works
A square is the odd one out and the sheets treat it that way. Stepping the radius cannot produce four points, so the square is built from a diameter and the perpendicular bisector of that diameter — two diameters at right angles, meeting the circle at the four corners. Meeting all three on one sheet is what makes the difference visible.
How this one works
One question from a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.
Inscribe a regular polygon, step by step