Final answer:
To use ASA postulate for proving triangle congruence, you need congruent angles and a shared side. Option B) Vertical angles and Corresponding angles are necessary for this proof as vertical angles are congruent and corresponding angles may also be congruent if part of the given triangles.
Step-by-step explanation:
To prove two triangles are congruent by the Angle-Side-Angle (ASA) postulate, you need to have two angles and the included side that are congruent. In the context of congruence postulates and theorems, alternate interior angles or corresponding angles can often be congruent due to parallel lines cut by a transversal. However, for ASA congruence specifically in a given figure, we are usually looking for angles that are parts of the triangles being compared.
In geometry, vertical angles are always congruent, and if a side is shared between two triangles, it is congruent to itself due to the reflexive property. Therefore, option B) Vertical angles and Corresponding angles allows us to use the ASA postulate for proving triangle congruence in the figure described, assuming the corresponding angles are indeed part of the triangles in question.
If two sets of alternate interior angles are congruent, that could imply congruence between the triangles if the angles are part of the triangles' corners, but the question does not make it clear that they are part of the triangles themselves. Therefore, option C) is less certain without more context around the figure.