Algebra

Substitution

CPCTC

DB = EB

Substitution

SSS (Side-Side-Side)

AB = CB, DA = EC

Triangle DAC = Triangle ECA

<A = <C

AE = CD

DA + DB = EC + EB

Reflexive

CPCTC

SAS (Side-Angle-Side)

Triangle DBC = Triangle EBA

AB = DA + DB and CB = EC + EB

Reflexive

CB = DA + DB

EC + DB = EC + EB

<B = <B

AC = AC

Given

Segment addition theorem

Substitution