△DBC = △EBA

Reflexive

Reflexive

AE = CD

CPCTC

Substitution

AB = DA + DB and CB = EC + EB

Substitution

∠A = ∠C

△DAC = △ECA

CPCTC

SSS (Side-Side-Side)

AB = CB, DA = EC

DA + DB = EC + EB

Algebra

DB = EB

SAS (Side-Angle-Side)

CB = DA + DB

EC + DB = EC + EB

∠B = ∠B

AC = AC

Given

Segment addition theorem

Substitution