Given: AB = CB, DA = EC

Prove: ∠A = ∠C

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