

Triangle given two angles and the included side (ASA)
Geometry construction using a compass and straightedge
This page shows how to construct a
triangle
given one side and the angle at each end of it with compass and straightedge or ruler. It works by first
copying the line segment
to form one side of the triangle, then
copy the two angles
on to each end of it to complete the triangle. As noted below, there are four possible triangles that be drawn  they are all correct.
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.
Note: this is not always possible
It is not always possible to construct a triangle from a given side length and two angles.
See figure on the right. If the two given angles add to more than 180°, the sides of the triangle will diverge and never meet.
See Interior Angles of a Triangle.
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
The image below is the final drawing above with the red items added.

Argument 
Reason 
1 
Line segment JL is congruent to AB. 
Drawn with the same compass width. For proof see Copying a line segment 
2 
The angle KJL is congruent to the angle A 
Copied using the procedure shown in
Copying an angle. See that page for the proof. 
3 
The angle KLJ is congruent to the angle B 
Copied using the procedure shown in
Copying an angle. See that page for the proof. 
4 
Triangle JKL satisfies the side length and two angle measure given.
 
 Q.E.D
Try it yourself
Click here for a printable worksheet containing two ASA 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.
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Other constructions pages on this site
Lines
Angles
Triangles
Right triangles
Triangle Centers
Circles, Arcs and Ellipses
Polygons
NonEuclidean constructions
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