DA + DB = EC + EB

Reflexive

△DBC = △EBA

AE = CD

CPCTC

∠A = ∠C

Reflexive

AB = CB, DA = EC

SAS (Side-Angle-Side)

Substitution

CPCTC

AB = DA + DB and CB = EC + EB

Algebra

SSS (Side-Side-Side)

△DAC = △ECA

Substitution

DB = EB

CB = DA + DB

EC + DB = EC + EB

∠B = ∠B

AC = AC

Given

Segment addition theorem

Substitution