As shown in the figure, it is known that ∠ B = ∠ C. If ad ‖ BC, does ad divide ∠ EAC equally? Please give reasons

As shown in the figure, it is known that ∠ B = ∠ C. If ad ‖ BC, does ad divide ∠ EAC equally? Please give reasons

Ad bisecting ∠ EAC for the following reasons: ∵ ad ‖ BC, (known) ∵ B = ∠ ead, (two parallel lines, equal angles) ∵ C = ∠ DAC, (two parallel lines, equal angles) ∵ B = ∠ C, (known) ∵ ead = ∠ DAC. (equivalent substitution) ∵ ad bisecting ∠ EAC. (definition of angle bisecting line)