Question

In ∆ABC and ∆DEF, it is given that $\frac{AB}{DE}=\frac{BC}{FD},$ then
(a) ∠B = ∠E
(b) ∠A = ∠D
(c) ∠B = ∠D
(d) ∠F = ∠F

Answer 1

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

$$\begin{gathered} \mathbf{Disclaimer}:\mathrm{In}\mathrm{the}\mathrm{question},\mathrm{the}\mathrm{ratio}\mathrm{should}\mathrm{be}\frac{AB}{DE}=\frac{BC}{FD}=\frac{AC}{EF}. \\ \mathrm{We}\mathrm{can}\mathrm{write}\mathrm{it}\mathrm{as}: \\ \frac{AB}{ED}=\frac{BC}{DF}=\frac{AC}{FE} \\ \mathrm{Therefore},△ABC~EDF \\ \mathrm{Hence},\mathrm{the}\mathrm{corresponding}\mathrm{angles},\mathrm{i}.\mathrm{e}.,\angle B\mathrm{and}\angle D,\mathrm{will}\mathrm{be}\mathrm{equal}. \\ \mathrm{i}.\mathrm{e}.,\angle B=\angle D \end{gathered}$$