Final answer:
To prove triangle congruence, theorems like SAS or ASA can be used, requiring corresponding sides and angles to match. The provided information does not pertain to △MNO or △XYZ's congruence, so additional relevant data is needed to provide a proof.
Step-by-step explanation:
To prove that △MNO is congruent to △XYZ, one would need to establish that there is a one-to-one correspondence between the vertices of the two triangles that preserves both angle measures and side lengths. This could involve showing that the two triangles satisfy one of the congruence postulates or theorems, such as the Side-Angle-Side (SAS) congruence theorem or the Angle-Side-Angle (ASA) congruence theorem.
However, the given information seems unrelated to the proof of congruence between △MNO and △XYZ. Details about lunar observations and relationships between heat gained and lost by substances do not contribute to geometric proofs of congruence between two specific triangles. Without additional geometric information connecting △MNO to △XYZ, we cannot reasonably conclude that the triangles are congruent. In this case, it would be best to request the necessary geometric details that relate directly to the triangles in question.