Final answer:
The Consecutive Interior Angles Converse Postulate is used to prove that two lines are parallel when given that a pair of consecutive interior angles are supplementary.
Step-by-step explanation:
To identify the postulate or theorem that proves two lines are parallel (p∥q) when given that angles 3 and 7 are supplementary, we refer to the Consecutive Interior Angles Converse Postulate.
This postulate states that if two lines are cut by a transversal and the consecutive interior angles add up to 180 degrees, then the lines are parallel. Since angles 3 and 7 are supplementary, they add up to 180 degrees and thus fulfill the condition of this postulate, proving that lines p and q are parallel.