CPCTC

AE = CD

∠A = ∠C

△DBC = △EBA

AB = DA + DB and CB = EC + EB

Reflexive

△DAC = △ECA

DB = EB

Substitution

Substitution

SAS (Side-Angle-Side)

Algebra

Reflexive

DA + DB = EC + EB

AB = CB, DA = EC

CPCTC

SSS (Side-Side-Side)

CB = DA + DB

EC + DB = EC + EB

∠B = ∠B

AC = AC

Given

Segment addition theorem

Substitution