
Triangle given two angles and a nonincluded side (AAS)
This page shows how to construct a
triangle
given two angles and a nonincluded side with compasses and straightedge or ruler.
The construction has four main parts:
 The given line segment AB is copied. See Copying a line segment.
 The given angle A is copied to one end of AB. See Copying an angle.
 The given angle C is copied to be adjacent to the angle A. This in effect adds A and C.
 The third angle created at A must be the angle B because the three angles at A add to 180, so this is copied to the point B. This in turn establishes point C and the triangle is complete.
How it works
The image below is the final drawing above.
The construction involves finding the angle B in the triangle. We know where this angle has to go (on the end of AB at point B),
but we must first find it's measure.
This is done by using constructions that add the given angles A and C,
then subtracting the result from 180.
Because the interior angles of a triangle add to 180, this must be the missing third angle B.
Proof
 Q.E.D
Multiple triangles possible
It is possible to draw more than one triangle has the side length and angle measures as given.
Depending on which end of the line you draw the angles, and whether they are above or below the line,
four triangles are possible.
All four are correct in that they satisfy the requirements, and are
congruent to each other.
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.
Try it yourself
Click here for a printable worksheet containing two AAS triangle construction 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) 2011 Copyright Math Open Reference. All rights reserved

