Problem 1
We have two possible answers here.
Either AC = DF is needed, or AB = DE is needed
We can't use BC = EF, as that would be ASA. The sides cannot be between the marked angles. With AAS, the sides are not between the angles.
Note: AC pairs up with DF because both segments have an endpoint at an angle with one arc marking. AB pairs up with DE because one endpoint has a double arc marking.
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Problem 2
We have a pair of congruent sides (due to the tickmarks) and a pair of congruent angles. We need another pair of angles. We can't pick angle B = angle E, as that would give us ASA. So we must pick the other pair of angles
angle A = angle D
If angle A = angle D, then we have enough to use AAS.
