Choose the correct answer from the given four options:
If in triangles $ \mathrm{ABC} $ and $ \mathrm{DEF}, \frac{\mathrm{AB}}{\mathrm{DE}}=\frac{\mathrm{BC}}{\mathrm{FD}} $, then they will be similar, when
(A) $ \angle \mathrm{B}=\angle \mathrm{E} $
(B) $ \angle \mathrm{A}=\angle \mathrm{D} $
(C) $ \angle \mathrm{B}=\angle \mathrm{D} $
(D) $ \angle \mathrm{A}=\angle \mathrm{F} $

Given:

In triangles \( \mathrm{ABC} \) and \( \mathrm{DEF}, \frac{\mathrm{AB}}{\mathrm{DE}}=\frac{\mathrm{BC}}{\mathrm{FD}} \).

To do:

We have to choose the correct answer.

Solution:

Given,

$\frac{\mathrm{AB}}{\mathrm{DE}}=\frac{\mathrm{BC}}{\mathrm{FD}}$

By converse of basic proportionality theorem,

If $\mathrm{ABC} \sim \mathrm{DEF}$, then,

$\angle \mathrm{B}=\angle \mathrm{D}$

$\angle \mathrm{A}=\angle \mathrm{E}$

$\angle \mathrm{C}=\angle \mathrm{F}$

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Updated on: 10-Oct-2022

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