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Angles You Built

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 39 of 61.

A constructed figure comes with its angles. Two circles of radius AB make an equilateral triangle, and every angle of an equilateral triangle is 60°, so the construction hands you 60° angles without a protractor.

$The constructed triangle PQR with its 60 degree angle at P$

In the figure, ∠RPQ is 60° by the rule Equilateral triangle: the circles make all three sides equal. From there the angle rules you already know reach further, to angles beside the triangle, on straight lines and around points.

Challenge

C was constructed from the circle about A through B and the circle about B through A, and the line AB runs on to D. Find ∠DBC, then press Check.

Try it yourself

$Find the marked part of the figure$

Find the marked part of the figure

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 MatchAngles You BuiltA 60° Angle Recap: Equilateral Triangle

11Constructed Shapes

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