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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