Question

In the figure, if CD/DA = CE/EB and angleCDE = angleCED Prove that triangleCAB is isosceles.

Standard:- 10th

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Answer 1

$\bold{\texttt{Given :-}}$

$\large{\mathtt{\frac{CD}{DA} = \frac{CE}{EB}}}$

$\mathtt{\angle CDE = \angle CED}$

$\bold{\texttt{To Prove :-}}$

$\texttt{∆CAB is isos. ∆}$

$\bold{\texttt{Proof :-}}$

$\texttt{In ∆CAB,}$

$\large{\mathtt{\frac{CD}{DA} = \frac{CE}{EB}}}$

$\therefore \texttt{DE || AB}$

$\because \texttt{DE || AB}$

$\therefore \mathtt{\angle CED = \angle CBA \;\;\; \& \angle CDE = \angle CAB}$

$\implies \mathtt{ \angle CBA = \angle CDE}$

$\because \mathtt{ \angle CBA = \angle CDE}$

$\therefore \texttt{∆CAB is isos. ∆}$