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

Answer

Correct option: C.
$\angle\text{B}=\angle\text{D}$
Given, in $\triangle\text{ABC}\text{ and }\triangle\text{DEF},$
$\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{FD}}$

Here, Angle formed by DE and FD is $\angle\text{D}.$
So, $\angle\text{B}=\angle\text{D}$
$\Rightarrow\text{DABC}\sim\text{DEDF}$

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