# Construction of an SSA Triangle

Construction of an SSA Triangle

A triangle is determined and constructible with ruler and compass if enough is known about its sides and angles; for example, where S and A mean side and angle, knowing SSS, SAS, ASA and AAS determines a triangle. The order is important: SSA can lead to two different triangles, depending on where the angle is located relative to the two given sides.

This Demonstration deals with the SSA case. It shows the construction of triangle given , and the angle at vertex . Assume that the side is already drawn.

ABC

c=AB

a=BC

γ

C

AB

Construct a straight line (shown dashed) through at an angle relative to . Let be the intersection of this line with the bisector of (also shown dashed). Then (after some thought), . The chord subtends the angle from the circle with center and radius .

A

90°-γ

AB

S

AB

∠ASB=2γ

AB

γ

σ

S

AS

The point is the intersection of and the circle with center and radius .

C

σ

B

a