
Flowchart or List of Steps
How to Determine the Number of Possible Triangles:
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When you are given an ASA (angle, side, angle) or an AAS (angle, angle, side) triangle
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There is only one possible triange
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If you given a SSA (side, side, angle) triangle things become more interesting. There can be either 0, 1, or 2 triangles.
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​Calculate the measure of another angle in the triangle using Law of Sines for angle measure.
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Add the measure of the given angle plus the measure of the calculated angle. Is the sum less than 180 degrees?
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No? Then there are no possible triangles that can be made with the given sides and angles.
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Yes? There is at least one possible triangle.
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Is the measure of the angle calculated greater than the measure of the given angle?
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No? Then there is only one possible triangle.
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Yes? There is a second possible triangle
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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.