So BD=CD

DE⊥AB，DF⊥AC，DE=DF，

So△ bed congruence △CFD(HL)

So ∠B=∠D

So AB=AC

2. Because BD⊥AC is in D, CE⊥AB is in E, BD=CE, BC=BC.

So △BEC congruence△ △CDB(HL)

So ∠ABC=∠ACB

So △ABC says isosceles triangle

3.OE vertically divides AB

Because AB=BA, ∠BAC=∠ABD, AC=BD,

So △DAB congruence△ △CBA(SAS)

So ∠DAB=∠CBA

Point e is the midpoint of AB,

So OE bisects AB vertically (isosceles triangle with three lines combined into one)