As shown in the figure, in the parallelogram ABCD, the bisector of ∠ ABC intersects CD at point E, and the bisector of ∠ ADC intersects AB at point F. try to judge whether AF and CE are equal, and explain the reason

As shown in the figure, in the parallelogram ABCD, the bisector of ∠ ABC intersects CD at point E, and the bisector of ∠ ADC intersects AB at point F. try to judge whether AF and CE are equal, and explain the reason


AF = CE. The reasons are as follows: ∵ quadrilateral ABCD is a parallelogram, ∵ ad = CB, ∵ a = C, ∵ ADC = ABC, and ∵ ADF = 12 ≌ ADC, ∵ CBE = 12 ≌ ABC, ∵ ADF = CBE. In △ ADF and △ CBE,