(1) Xiaoying proposed: As shown in Figure 2, if "point E is the midpoint of BC" is changed to "point E is any point on BC (except B and C)", other conditions remain unchanged, then the conclusion "AE=EF" still holds. Do you think Xiaoying's point of view is correct? If it is correct, write the proof process; If not, please explain the reasons;
(2) Xiaohua proposed that, as shown in Figure 3, point E is a point on the BC extension line (except point C), and the conclusion of "AE=EF" still holds, with other conditions unchanged. Do you think Xiaohua's view is correct? If it is correct, write the proof process; If not, please explain why. Solution: (1) is correct.
Proof: Take a little M from AB to make am = EC, and connect me.
∴BM=BE.∴∠BME=45。 ∴∠AME= 135。
∫CF is the bisector of the outer corner,
∴∠DCF=45。 ∴∠ECF= 135。
∴∠AME=∠ECF.
∠∠AEB+∠BAE = 90,∠AEB+CEF=90,
∴∠BAE=∠CEF.
∴△AME≌△BCF(ASA).
∴AE=EF.
(2) correct.
Proof: Take a little n on the extension line of BA, make an = ce, and then connect ne.
∴BN=BE.
∴∠N=∠FCE=45。
The quadrilateral ABCD is a square,
∴AD‖BE.
∴∠DAE=∠BEA.
∴∠NAE=∠CEF.
∴△ANE≌△ECF(ASA).
∴AE=EF.