What condition is required by the ASA theorem for two triangles to be congruent?

The ASA theorem, which stands for Angle-Side-Angle, specifies that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent. This means that the triangles have the same shape and size.

In the ASA condition, the "included side" refers to the side that is positioned between the two angles. Ensuring that both angles are equal and that the side they encompass is equal ensures that the triangles are identical in shape and size. This congruence assertion is significant because it allows for the establishment of equal relationships between corresponding sides and angles of the triangles, confirming their congruence.

The other options do not fulfill the requirements set forth by the ASA theorem. For instance, while having all angles equal signifies similarity, it does not guarantee congruence unless accompanying side measures are included. Similarly, proportional sides or an angle with a non-included side do not comply with the specific criteria that the ASA theorem establishes.