Question

in the given figure , c is the midpoint of AB . If angle DCA = angle ECB and angle DBC = angle EAC , prove that DC = EC.
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Answer 1

Answer:

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Answer 2

Hi mate here is the 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

Hope it helps you ❣️☑️☑️☑️