∠A = ∠C

Substitution

SAS (Side-Angle-Side)

DA + DB = EC + EB

△DBC = △EBA

AB = DA + DB and CB = EC + EB

Reflexive

CPCTC

DB = EB

Reflexive

Algebra

Substitution

SSS (Side-Side-Side)

CPCTC

△DAC = △ECA

AE = CD

AB = CB, DA = EC

CB = DA + DB

EC + DB = EC + EB

∠B = ∠B

AC = AC

Given

Segment addition theorem

Substitution