In the given figure, FEC GDB and 1= 2. Prove that ADE ABC. - Vidyadip

Question

In the given figure, $\triangle FEC \cong \triangle GDB$ and $\angle 1=\angle 2$. Prove that $\triangle ADE \sim \triangle ABC$.

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Answer

$\Delta FEC \cong \Delta GDB$
Therefore, $\angle 3=\angle 4$
In $\triangle ABC$,
$\angle 3 =\angle 4$
$\therefore AB =AC.......(i)$
In $\triangle ADE , \angle 1=\angle 2$
$AD=AE......(ii)$
Dividing $(ii)$ by $(i)$
$\frac{AD}{AB}=\frac{AE}{AC}$
$\Rightarrow DE \| BC$
$\angle 1=\angle 3 \text { and } \angle 2=\angle 4$
$\therefore \triangle ADE \sim \triangle ABC$

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