Answer :

It is given that AC = BC , DCA = ECB and DBC = EAC.


Adding angle ECD both sides in DCA = ECB, we get,


DCA + ECD = ECB + ECD


∴∠ECA = DCB …addition property


Now in ΔDBC and ΔEAC,


ECA = DCB


BC = AC


DBC = EAC


Hence by ASA postulate, we conclude,


ΔDBC ΔEAC


Hence, by cpct, we get,


DC = EC


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