I believe it is AAS but am not sure whether ASA could be true as well

Choice C) AAS

Nice work on getting the correct answer.

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Explanation:

We're given that angle A = angle C. This is shown in green in the diagram below.

AB || DC so we can show that angle ABD = angle CDB by the alternate interior angle theorem. This is shown in red.

Finally, we know that BD = BD which is marked in blue.

Note how the blue segment is not between the red and green angle for any of the two triangles. So we use AAS instead of ASA. The order is important.

your answer would be 12