Given: AB = CB, DA = EC

Prove: ∠A = ∠C

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