Congruent Triangles - Why SSA doesn't work

Given two sides and non-included angle (SSA) is not enough to prove congruence.

Try this Click on the "other triangle" under the triangle on the right.

You may be tempted to think that given two sides and a non-included angle is enough to prove congruence. But there are two triangles possible that have the same values, so SSA is not sufficient to prove congruence.

In the figure above, the two triangles above are initially congruent. But if you click on "Show other triangle" you will see that there is another triangle that is not congruent but that still satisfies the SSA condition. AB is the same length as PQ, BC is the same length as QR, and the angle A is the same measure as P. And yet the triangles are clearly not congruent - they have a different shape and size.

So I can't use SSA at all?

On its own - no. But you could use it if you also provide proof as to which of the two possible triangles are described.

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