Problem

Name the congruence criterion and decide whether this is enough information to prove triangle congruence: \(\text{two}~\text{sides}\) and the included angle match.

Triangle or coordinate diagram presenting only the geometric data supplied in the prompt.

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What this problem is really about

Start by locating the marked angle relative to the two marked sides; its placement is what distinguishes a valid rigid triangle pattern from ambiguous side-side-angle information. When that angle lies between the known sides, aligning one side and rotating the other into place fixes the third vertex as well.

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This is SAS, but it is still not enough information because you need all three sides or all three angles to prove congruence.

This is AAA, and it is not enough information to prove the triangles are congruent because matching angles only shows the triangles are similar.

This is SAS, and it is enough information to prove the triangles are congruent because the angle is included between the two sides.

This is SSA, and it is not enough information to prove the triangles are congruent because two sides and one angle can be ambiguous.

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Name the congruence criterion and decide whether this is enough information to prove triangle congruence: \(\text{two}~\text{sides}\) and the included angle match.

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