E and d are the midpoint of AB and AC respectively (known).

∴AE= 1/2AB, AD= 1/2AC (definition of midpoint)

AB = AC (known)

∴AE=AD (equivalent substitution)

In △ABD and △ACE,

AB=AC (known)

∠A=∠A (angle * * *)

AE=AD (certification)

∴△ABD≌△ACE(SAS)

(2) By (1)

∫△ABD?△ACE

∴∠ADB=∠AEC (the corresponding angles of congruent triangles are equal).

∠∠ADB+∠BDC = 180, ∠ AEC+∠ BEC = 180 (as shown in the figure).

∴∠BDC=∠BEC (complementary angles of equal angles are equal)

(3) By (1)

∫△ABD?△ACE

∴∠ABD=∠ACE (the angles corresponding to congruent triangles are equal), BD=CE (the sides corresponding to congruent triangles are equal).

AB = AC

∴∠ABC =∞∠ACB (equilateral and equiangular)

∴∠ABC-∠ABD=∠ACB-∠AC

∠OBC=∠OCB (equivalent substitution)

∴OB=OC (equilateral)

∴BD-OB=CE-OC

OD=OE