E 5 Use the information given in the adjoining figure, to prove : (i) A DBC = A EAC. (ii) DC = = EC. A + B C
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In given figure,
AC=BC,
∠EAC=∠DBC
And, ∠BCE=∠ACD
From figure ∠ACE=∠DCE+∠ACD
And ∠BCD=∠DCE+∠BCE
But, given in figure ∠ACD=∠BCE=x
∴∠BCD=∠ACE
In ΔDBC and ΔEAC
∠BDC=∠ACE
BC=AC
∠DBC=∠EAC
(i) ∴ΔDBC≅ΔEAC ....SAA test
Then, DC=EC
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