Given: AB = CB, DA = EC

Prove: <A = <C

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