Is the solution to the the triangle congruency problem correct?

GRE Quant Problem Solving
1

I was going through this problem in the Solve Quant Area:

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According to the solution:
“One side and two angles of A equaling one side and two angles of B” is marked correct based on AAS but AAS specifically applies only when this equal side of the two triangles has to be the corresponding non-included side only.

In fact, in another question in the quant section there is this example:
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Here, all 3 angles are equal (90, 60, 30) and one side is equal → AB = BD but these are not congruent.
Just to be clear, I am not asking/saying they should be congruent here. This example shows that even when the criteria:
“One side and two angles of A equaling one side and two angles of B” is satisfied, congruency is not guaranteed and only guaranteed when the corresponding non-included side is equal. So, this option should be incorrect in the multi-choice question above.

Apologies if this is a repeat question.

2

The problem is that the angles are not actually equal. In \Delta BDE, the corresponding angles are 60 and 30 degrees, while it’s the other way round for \Delta ABC. You can apply AAS only when the corresponding angles are equal.

3

Yes, I agree with that but the option in the question is ambiguous at best then because it says:
“One side and two angles of A equaling one side and two angles of B”

This specific criteria is satisfied by the example but it is not congruent, so this option should be incorrect

4

You are right, the question has been taken down for now as a result as it has been flagged for review.