Given: AB = CB, DA = EC

Prove: ∠A = ∠C

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