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Copying an Angle
Geometry construction using a compass and straightedge

Given an angle formed by two lines with a common vertex, this page shows how to construct another angle from it that has the same angle measure using a compass and straightedge or ruler. It works by creating two congruent triangles. A proof is shown below.

Printable step-by-step instructions

The above animation is available as a printable step-by-step instruction sheet, which can be used for making handouts or when a computer is not available.

Proof

This construction works by creating two congruent triangles. The angle to be copied has the same measure in both triangles

The image below is the final drawing above with the red items added.

  Argument Reason
1 Line segments AK, PM are congruent Both drawn with the same compass width.
2 Line segments AJ, PL are congruent Both drawn with the same compass width.
3 Line segments JK, LM are congruent Both drawn with the same compass width.
4 Triangles ∆AJK and ∆PLM are congruent Three sides congruent (SSS).
5 Angles BAC, RPQ are congruent. CPCTC. Corresponding parts of congruent triangles are congruent

  - Q.E.D

Try it yourself

Click here for a printable worksheet containing two angle copying problems. When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.
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Other constructions pages on this site

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Arcs and Ellipses

Polygons

Non-Euclidean constructions