
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 stepbystep instructions
The above animation is available as a
printable stepbystep 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.
Other constructions pages on this site
Lines
Angles
Triangles
Right triangles
Triangle Centers
Circles, Arcs and Ellipses
Polygons
NonEuclidean constructions
(C) 2009 Copyright Math Open Reference. All rights reserved

