What additional information is required to prove that the triangles are congruent using the ASA (Angle-Side-Angle) Postulate? Is angle NL congruent to angle MP, is angle NK congruent to angle MQ, or is side N congruent to side M, or is side L congruent to side P?

To prove that two triangles are congruent using the Angle-Side-Angle (ASA) Postulate, you need to establish that two angles and the side between them in one triangle are congruent to two angles and the side between them in the other triangle. In other words, you need to know that:

1. One angle in the first triangle is congruent to one angle in the second triangle.

2. The side between the two angles in the first triangle is congruent to the side between the two angles in the second triangle.

3. The other angle in the first triangle is congruent to the corresponding angle in the second triangle.

If you have already established that one pair of corresponding angles is congruent, you now need to confirm that the included side (the side between the two angles) is congruent and then demonstrate that the second angle is congruent.

So, in your case, assuming angle N corresponds to angle M and you want to apply the ASA Postulate, you would need:

• Angle NL to be congruent to angle MP (if angle L corresponds to angle P) or angle NK to be congruent to angle MQ (if angle K corresponds to angle Q), depending on which angles are actually being compared.
• And the side between the angles you've been comparing (side N in the first triangle and side M in the second triangle, for instance) needs to be congruent as well.

To summarize, if angle N is indeed congruent to angle M, then to prove the triangles congruent by ASA, you would need to also establish that:

• Either angle NL is congruent to angle MP or angle NK is congruent to angle MQ (whichever are the corresponding angles).
• The side between angles N and L or N and K (whichever was relevant to the angle you established) is congruent to the side between angles M and P or M and Q in the other triangle.