Based on the information provided, the most relevant statement that could be proved using a diagram involving angles formed by parallel lines and a transversal would be: Alternate interior angles are congruent.
If the diagram depicts two parallel lines cut by a transversal, it directly supports the proof that alternate interior angles are congruent. Other statements, like the Triangle Angle Sum Theorem or the Pythagorean Theorem, typically require different types of diagrams or configurations to prove, and the statement about parallel lines having the same slope is more of a definition than a theorem to prove.
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