Given: AB = CB, DA = EC

Prove: ∠A = ∠C

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