Question

Use the information given in the adjoining figure, to prove:
(i) $△DBC\cong △EAC$
(ii) $DC=EC$

Answer 1

In given figure,

$AC=BC$,

$\angle EAC=\angle DBC$

And, $\angle BCE=\angle ACD$

From figure $\angle ACE=\angle DCE+\angle ACD$

And $\angle BCD=\angle DCE+\angle BCE$

But, given in figure $\angle ACD=\angle BCE=x$

$\therefore \angle BCD=\angle ACE$

In $\Delta DBC$ and $\Delta EAC$

$\angle BDC=\angle ACE$

$BC=AC$

$\angle DBC=\angle EAC$

(i) $\therefore \Delta DBC\cong \Delta EAC$ ....SAA test

Then, $DC=EC$