Given: AB = CB, DA = EC

Prove: ∠A = ∠C

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