As shown in the figure, ab = AE, BC = ed, ∠ B = ∠ e, AF ⊥ CD, foot drop is f, which means that AF bisects CD

As shown in the figure, ab = AE, BC = ed, ∠ B = ∠ e, AF ⊥ CD, foot drop is f, which means that AF bisects CD

Make auxiliary line AC, ad
Because AB = AE, BC = ed, ∠ B = e (edge)
So triangle ABC = triangle AED (congruent)
So AC = ad
So triangle ACD is isosceles triangle
Therefore, ACF = ADF
Because AF ⊥ CD
Therefore, AFC = AFD = 90 degree
Because AC = ad, ACF = ADF, AFC = AFD (corner side)
So triangle AFC = triangle AFD (congruent)
So CF = DF