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Question

In the given figure, C is the mid-point of AB. If ∠DCA = ∠ECB and ∠DBC = ∠EAC, prove that DC = EC.
Figure

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Solution

In ECA and DCB,EAC=DBC given AC = BC C is the mid point of ABNow,DCA= ECBDCA + DCE= ECB + DCEACE= BCDTherefore, by ASA congruency criteria, ECA DCB. DC = EC Corresponding sides of congruent triangles are equal

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