In the given figure, ABC = ACB and B C B E =B D A C . Show that A… - Vidyadip

Question

In the given figure, $\angle ABC =\angle ACB$ and $\frac{B C}{B E}=\frac{B D}{A C}$.

Show that $\angle ABE \sim \angle DBC$ and $AE \| DC$.

✓

Answer

It is given that $\frac{B C}{B E}=\frac{B D}{A C}$
$\Rightarrow \frac{B E}{B C}=\frac{A B}{D B}$
$(\because \angle ABC=\angle ACB \Rightarrow AC=AB)$
Also $\angle B$ is common
$\therefore \triangle ABE \sim \triangle DBC \text { (SAS}$ similarity$)$
$\Rightarrow \angle BAE=\angle BDC$
But these are corresponding angles $\therefore AE \| DC$.

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