Final answer:
To prove that lines are parallel based on a transversal and angle measures, typically you would use properties of corresponding or alternate interior angles. However, in this case, we do not have enough information to prove that line a is parallel to line b solely based on the given angle measurements.
Step-by-step explanation:
To solve the geometry problem stating that transversal c intersects lines a and b, and to prove that line a is parallel to line b (a || b), given that m∠3 = 45 degrees and m∠5 = 3 × m∠3, we need to use the properties of parallel lines and the angles formed by a transversal.
Given that m∠3 = 45 degrees, we can immediately state that m∠5 = 135 degrees (because m∠5 = 3 × 45 deg). Considering the properties of corresponding angles and alternate interior angles, if lines a and b are cut by a transversal and the corresponding angles are equal (or the alternate interior angles are equal), then lines a and b are parallel.
In this problem, if m∠3 corresponds with m∠5 on parallel lines, it would mean that m∠3 + m∠5 = 180 degrees, making these two angles supplementary. However, since this is not the case (45 + 135 = 180 is true, but it doesn't prove correlation or alternation), we do not have enough information to conclude that line a is parallel to line b based solely on the given information. Therefore, we cannot prove that line a is parallel to line b with the information given.