The correct option is A True
Let us extend AB. Then, draw a line through C, which is parallel to AD, intersecting AE at point E. It is clear that AECD is a parallelogram.
AD = CE (Opposite sides of parallelogram AECD)
However, AD = BC (Given)
Therefore, BC = CE
∠CEB=∠CBE
∠CBE+∠CBA=180∘ (Linear pair)………….(1)
∠CBA+∠DAB=180 (Angles on the same side of transversal)……….(2)
From (1) and (2) ∠A=∠B