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Constructing a triangle given two angles and included side (ASA)

This is the step-by-step, printable version. If you PRINT this page, any ads will not be printed.

See also the animated version.

After doing this Your work should look like this

Start with the given line segment and two angles.

Geometry construction with compass and straightedge or ruler or ruler
Note: The two given angles are only there to indicate the measure of the two angles. The lines making up the given angles have random lengths that have no significance in the construction.
The first part of this construction (steps 1 - 4) is to copy a line segment to form one side of the new triangle. (See Copying a Line Segment).
1.  Mark a point A that will be one vertex of the new triangle. Geometry construction with compass and straightedge or ruler or ruler
2.  Set the compasses' width to the length of the segment AB. Geometry construction with compass and straightedge or ruler or ruler
3.  With the compasses' point on A, make an arc near the future vertex B of the triangle. Geometry construction with compass and straightedge or ruler or ruler
4.  Mark a point B on this arc. Then draw the line AB. This will be one side of the new triangle. Geometry construction with compass and straightedge or ruler or ruler
What we do now is essentially copy the two angles. (See Copying an Angle).
5.  With the compasses at any convenient width, draw an arc across both lines of the given angle A. Geometry construction with compass and straightedge or ruler or ruler
6.  Without changing the compasses' width, draw an arc at point A on the new triangle. The arc must cross AB and also cross the future side of the triangle. Geometry construction with compass and straightedge or ruler or ruler
7.  Set the compasses to the arc width at the given angle A. This the distance between the points where the arc intersects the sides of the angle. Geometry construction with compass and straightedge or ruler or ruler
8.  Near point A draw an arc in a similar position so it crosses the arc drawn earlier. This, in effect, 'copies' the measure of the angle at P to the angle at A. Geometry construction with compass and straightedge or ruler or ruler
9.  Draw a line from A through the point where the arcs intersect. This will become the second side of the triangle. Draw it long. Geometry construction with compass and straightedge or ruler or ruler
10.  Repeat this process at B. Copying the angle measure from the given angle B to the new triangle at B. The point where the lines intersect is C, the third vertex of the triangle. Geometry construction with compass and straightedge or ruler or ruler
Done. The blue triangle ABC has the side and two angle measures desired.  

Other constructions pages on this site

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Arcs and Ellipses

Polygons

Non-Euclidean constructions