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Question

In given figure if AC = BC, DCA = ECB and DBC = EAC, then DC = __.

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Solution

We have,
DCA = ECB
DCA + ECD = ECB + ECD
ECA = DCB .......(i)

Now, in Δs DBC and EAC, we have
DCB = ECA [From (i)]
BC = AC [Given]
and DBC = EAC [Given]

So, by ASA criterion of congruence
ΔDBC ΔEAS
DC = EC [ Correcponding parts of congruent triangles are equal ]


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