How to Construct a Triangle When Given Two Angles & the Non-Included Side

Triangles are fun to play with.

Constructing a triangle from two angles and an included side is relatively easy. You simply copy one of the sides, including an angle at the endpoint of the side, and then mark off the length of the other side. This allows you to construct the third side. However, when you are given two angles and the non-included side, things get a little but trickier. But if you use the proof that all angles on a triangle must add up to 180 degrees, you can still construct the triangle using a ruler and compass.

Things You'll Need

• Pencil
• Paper
• Ruler
• Compass

Instructions

1. Mark off the non-included side as AB on the sheet of paper.

2. Make two copies of angle A, one with its vertex at A and one with its vertex at B. You should have two parallel diagonal lines that reach up from side AB.

3. Construct angle C at the vertex of the second angle A with side AB. Use the diagonal angle line of angle A as the base of angle C.

4. Angle C should intersect the diagonal line of the first angle A, giving you a triangle. Erase all other marking lines and you have your completed triangle.

References

• Ceemrr: Constucting Triangles
• University of Plymouth: Centre for Innovation in Mathematics Teaching: Constructions and Angles