Given: AB = CB, DA = EC

Prove: <A = <C

Substitution
SAS (Side-Angle-Side)
DB = EB
Algebra
AB = DA + DB and CB = EC + EB
Reflexive
Substitution
<A = <C
AE = CD
Triangle DBC = Triangle EBA
Triangle DAC = Triangle ECA
DA + DB = EC + EB
CPCTC
Reflexive
CPCTC
SSS (Side-Side-Side)
AB = CB, DA = EC
CB = DA + DB
EC + DB = EC + EB
<B = <B
AC = AC
Given
Segment addition theorem
Substitution