Known: as shown in the figure, points B, e, C, f are on the same line, ab = De, AC = DF, be = CF

Known: as shown in the figure, points B, e, C, f are on the same line, ab = De, AC = DF, be = CF

It is proved that: ∵ be = CF, ∵ BC = EF, ab = De, AC = DF, ≌ ABC ≌ def, ≌ B = ≌ def, ∥ ab ∥ de (the same angle, two lines parallel)

As shown in the figure, D is the point on AB, DF intersects AC at e, de = Fe, FC ‖ ab. try to judge the quantitative relationship between AE and CE? And prove your conclusion

AE = CE for the following reasons: it is proved that: ∵ FC ∥ AB, ∩ ade = ∩ F, (two straight lines are parallel and the internal stagger angle is equal), and ∵ de = Fe, ∩ AED = ∩ CEF, ≌ ade ≌ CFE (ASA), ∩ AE = CE

As shown in the figure, D is the point on AB, DF intersects AC at e, de = Fe, FC ‖ ab. try to judge the quantitative relationship between AE and CE? And prove your conclusion

AE = CE for the following reasons: it is proved that: ∵ FC ∥ AB, ∩ ade = ∩ F, (two straight lines are parallel and the internal stagger angle is equal), and ∵ de = Fe, ∩ AED = ∩ CEF, ≌ ade ≌ CFE (ASA), ∩ AE = CE

As shown in the figure on the previous page, D is the point on AB, DF intersects AC at the point E, de = Fe, FC ‖ AB, AE and CE. What is the relationship between them? Prove your conclusion?

AE = CE, reason: ∵ FC ∥ Fe, in △ ead and △ ECF, de = Fe ≌ AED = ≌ CEF ≌ DAE = ≌ ECB ≌ ECF ≌ AC = CE