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3. (1) 在△ABE和△ACD中,∵ ∠A = ∠A,∠B = ∠C,AE = AD,
∴△ABE ≌ △ACD(AAS).
(2)∵△ABE ≌ △ACD,
∴ AB = AC,AB - AD = AC - AE,即DB = EC.在△BOD和△COE中,
∵ ∠DOB = ∠EOC,∠B = ∠C, DB = EC,
∴ △BOD ≌ △COE(AAS).
1.3 探索三角形全等的条件(5)
1. ∵ B是EC的中点,
∴ BE = BC.
∵ ∠ABE = ∠DBC,
∴∠ABE + ∠ABD = ∠DBC + ∠ABD,
即∠DBE = ∠ABC.在△DEB和△ACB中,
∵ ∠DBE = ∠ABC,∠D = ∠A,
BE = BC,
∴ △DEB ≌ △ACB( AAS).
∴DE = AC.