Final answer:
To prove that angles 3 and 4 are complementary, additional information about their relationship to angles 1 and 2 is needed. As presented, none of the given options directly conclude that angles 3 and 4 are complementary since we lack sufficient context.
Step-by-step explanation:
To prove that angles 3 and 4 are complementary, we must first understand the definitions of complementary angles and how they relate to supplementary angles, congruent angles, and right angles.
Complementary angles are two angles whose sum is 90 degrees, while supplementary angles have a sum of 180 degrees.
If angles 3 and 4 are supplementary, as mentioned in option A, their sum would be 180 degrees. If they are congruent (option B), they are equal in measure to each other, which doesn't necessarily mean they are complementary.
Option C states that angles 3 and 4 are right angles, and a right angle is exactly 90 degrees, which would not allow them to be a pair since their sum would exceed 90 degrees. Lastly, if angles 3 and 4 are vertical angles (option D), they are congruent, but we still need to demonstrate that their measures sum to 90 degrees to prove they are complementary.
Without additional information given with the question, such as a diagram or further given angles, we cannot complete the formal proof. To reach a conclusion, more data about the relationship between angles 1, 2, 3, and 4 is required. As the question stands, none of the provided options A, B, C, or D directly lead us to proving that angles 3 and 4 are complementary without further context.