# In ∆ABC and ∆DEF, it is given that

Question:

In $\triangle A B C$ and $\triangle D E F$, it is given that $\frac{A B}{D E}=\frac{B C}{F D}$, then

(a) ∠B = ∠E
(b) ∠A = ∠D
(c) ∠B = ∠D
(d) ∠F = ∠F

Solution:

(c) $\angle B=\angle D$

Disclaimer: In the question, the ratio should be $\frac{A B}{D E}=\frac{B C}{F D}=\frac{A C}{E F}$.

We can write it as:

$\frac{A B}{E D}=\frac{B C}{D F}=\frac{A C}{F E}$

Therefore, $\triangle A B C \sim E D F$

Hence, the corresponding angles, i. e., $\angle B$ and $\angle D$, will be equal.

i. e., $\angle B=\angle D$