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Flowchart or List of Steps

How to Determine the Number of Possible Triangles:

  1. When you are given an ASA (angle, side, angle) or an AAS (angle, angle, side) triangle

    • There is only one possible triange

  2. If you given a SSA (side, side, angle) triangle things become more interesting. There can be either 0, 1, or 2 triangles.

    1. ​Calculate the measure of another angle in the triangle using Law of Sines for angle measure.








       

    2. Add the measure  of the given angle plus the measure of the calculated angle. Is the sum less than 180 degrees?

      • No? Then there are no possible triangles that can be made with the given sides and angles.

      • Yes? There is at least one possible triangle.

    3. Is the measure of the angle calculated greater than the measure of the given angle?

      • No? Then there is only one possible triangle.

      • Yes? There is a second possible triangle

Caption:

I thought that this list of steps was important to include due to the fact that determining the number of triangles can be a difficult process. Leaving out one of the triangles when two are present is a common mistake. With this list of steps, however, determining the number of triangles no longer needs to be such an ordeal.

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