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., $\angle B=\angle D$