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Half of 60°

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 45 of 61.

Bisecting a 60° angle gives 30°. There is a quick way that reuses the circles you already have, and it works for the same reason as the angle bisector: a shape that folds onto itself.

$Rhombus PQWR with its diagonal PW$

Build the 60° first: circles about P through Q and about Q through P cross at R. Now draw the circle about R through P. It meets the circle about Q again at W. Every side of PQWR is a radius of length PQ, so PQWR is a rhombus, and a diagonal of a rhombus halves the angle it starts from. The line PW halves the 60° angle QPR: it is at 30° to PQ.

Challenge

Construct a line through A at 30° to the ray AB, then press Check.

Try it yourself

$Construct it with a compass and straightedge$

Construct it with a compass and straightedge

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 Symmetry Regular Polygons Symmetry Is a Move Recap: Symmetry

9Bisectors

The Perpendicular Bisector The Midpoint Bisecting an AngleHalf 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