As shown in the figure, in △ ABC, D is the point on AB, DF intersects AC at e, de = Fe, AE = CE, what is the positional relationship between AB and CF? Prove your conclusion

As shown in the figure, in △ ABC, D is the point on AB, DF intersects AC at e, de = Fe, AE = CE, what is the positional relationship between AB and CF? Prove your conclusion

Ab ∥ cf. it is proved that ∵ AED and ≌ CEF are opposite vertex angles, ∥ AED = ∥ CEF. In △ ade and △ CFE, ∥ de = Fe, ∥ AED = ∥ CEF, AE = CE, ≌ ade ≌ CFE. ∥ a = ∥ FCE. ∥ ab ∥ CF

Ad is the bisector of the outer angle of the triangle ABC, CE is perpendicular to ad, EF is parallel to AB, AC intersects at point F, and AF = CF is proved

The conclusion should be BF = CF?
When CE is extended and Ba is crossed with G, then △ ace ≌ △ age (ASA), CE = Ge,
Because EF ‖ GB, BF = CF (a line passing through the midpoint of one side of the triangle and parallel to the second side bisects the third side)

As shown in the figure, in known triangle ABC, ab = AC, angle a = 36 degrees, BD bisecting angle ABC, EF bisecting angle ad vertically, respectively AB.AD For E.F., CE is perpendicular to BD

Then in ∠ ABC = ∠ ACB = 72 °△ BCD, ∠ CBD = ∠ ABC / 2 = 36 °∠ ACB = 72 °

As shown in the figure, in △ ABC, ad is the angular bisector, CE ⊥ ad, f is the midpoint of BC

It is proved that: as shown in the figure, extending CE intersection AB to g, ∵ ad is the angular bisector, ∵ EAG = ≁ EAC, ≁ CE ⊥ ad, ≁ AEG = ≁ AEC = 90 °, in △ age and △ ace, ≌ EAG = ≌ eacae ≌ AEG = ≌ AEC = 90 °, and ≌ Ag = AC, CE = Ge, and ≌ f is the midpoint of BC, ≁