# 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) $\angle \mathrm{A}=\angle \mathrm{F}$

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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,

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

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

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

Updated on 10-Oct-2022 13:27:54