 # Construction of an SSA Triangle

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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.

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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.

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 .

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

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Contributed by: Izidor Hafner (May 2017)
Open content licensed under CC BY-NC-SA

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Izidor Hafner

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