Answers:
Problem 1) ASA
Problem 2) ASA
Problem 3) AAS
Problem 4) Neither
Problem 5) AAS
Problem 6) Neither
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Explanation:
Any time we have ASA is when we can match up two pairs of angles and a pair of sides between the two pairs of angles. With problems 1 and 2, this happens. The corresponding angles that are congruent are the ones that have the same angle markers.
AAS is slightly different from ASA in that the side is not between the angles. This happens with problem 3 and problem 5. For problem 3, for instance, the second pair of angles are the two vertical angles. These angles are not marked, but they are congruent due to the vertical angle theorem. The same thing can be said about problem 5 as well.
With problem 4 and problem 6, we don't have any information about any pairs of angles, so we can't use AAS or ASA at all. We don't know if the triangles are congruent or not. They might be, but we simply don't have enough info to say either way.
