If in and , AB DE = BC FD , then when : - Vidyadip

MCQ

If in $\triangle\text{ABC}$ and $\triangle\text{DEF}, \frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{FD}},$ then $\triangle\text{ABC}\sim\triangle\text{DEF}$ when :

A
$\angle\text{A}=\angle\text{F}$
B
$\angle\text{A}=\angle\text{D}$
✓
$\angle\text{B}=\angle\text{D}$
D
$\angle\text{B}=\angle\text{E}$

✓

Answer

Correct option: C.

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

$\triangle\text{ABC}\sim\triangle\text{DEF}$
In $\triangle\text{ABC}$ and $\triangle\text{DEF},$
$\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{FD}}$
Then $\angle\text{B}=\angle\text{D} \ ($included angle $\text{SAS}$ axiom$)$.

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