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Answer 1 · 2018-02-16T13:15:12

I suppose option A $(△ A D E ~ △ A B C)$ $(triangleADE ~triangleABC)$ is correct.

this is because, it is already given that, $∠ D = ∠ B$ $color(magenta)(angleD = angleB$
$∠ A$ $color(magenta)(angle A$ is shared by both the triangles,

now,
$∠ E = 180^{\circ} - ∠ A - ∠ D$ $angle E = 180^@ - angleA - angle D$
$∠ C = 180^{\circ} - ∠ A - ∠ B$ $angle C = 180^@ - angleA - angle B$
$\Rightarrow ∠ E = ∠ C$ $=>color(magenta)(angle E =angle C$

Hence, since the corresponding angles are equal, the triangles are similar by, AAA rule

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