To determine whether the two triangles can be shown to be congruent using the Angle-Side-Angle (ASA) postulate, we need to check if we have two angle measurements and the included side.
From the options presented:
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The first option suggests using the triangle angle sum theorem to find a missing angle in the pink triangle. If you can determine the third angle based on the angles you already know and have two angles and the included side from one triangle to the corresponding elements in the other triangle, this would indicate that the triangles can be shown to be congruent using ASA.
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The second option states that there are 2 angle measurements given in each triangle and 1 side, which aligns with ASA theory as long as the side is between the two angles being considered.
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The third option outright states that they cannot be shown to be congruent with ASA, which would only be true if there were not sufficient angle and side data.
Based on the information that two angles and the included side can be utilized, the proper response would be:
Yes, because there are 2 angle measurements given in each triangle and 1 side.
This option confirms the conditions for applying the ASA congruence postulate.