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A 60° Angle

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 40 of 61.

The equilateral construction is also the way to build a 60° angle. If C is the third corner of an equilateral triangle on AB, then ∠CAB is 60°, so the line from A through C is at 60° to AB.

$A 60 degree angle at P built from two circles and a line$

To make a 60° angle at P on the ray PQ: draw the circle about P through Q and the circle about Q through P, take a point R where they cross, and draw the line PR. Three tools: two circles and one line. The Point you tap is free.

Challenge

Construct a line through A at 60° 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

2Reflections

Reflecting in a Line The Two Axes The Line y = x Find the Mirror Recap: Reflections

5Dilations

Scaling From a Center Shrinking a Shape Dilating About a Point Negative Scale Factors Recap: Dilations

8Compass and Straightedge

Circles Keep Distances Why the Sides Match Angles You BuiltA 60° AngleRecap: Equilateral Triangle

11Constructed Shapes

A Square on a Segment The Regular Hexagon Copy an Angle A Tangent From a Point Recap: Constructed Shapes