Question:
If in two triangles ABC and DEF, ABDE=BCFE=CAFD, then
(a) ∆FDE ∼ ∆CAB
(b) ∆FDE ∼ ∆ABC
(c) ∆CBA ∼ ∆FDE
(d) ∆BCA ∼ ∆FDE
Solution:
We know that if two triangles are similar if their corresponding sides are proportional.
It is given that $\triangle \mathrm{ABC}$ and $\triangle \mathrm{DEF}$ are two triangles such that $\frac{\mathrm{AB}}{\mathrm{DE}}=\frac{\mathrm{BC}}{\mathrm{EF}}=\frac{\mathrm{CA}}{\mathrm{FD}}$.
∠A=∠D∠B=∠E∠C=∠F
$\therefore \triangle \mathrm{CAB} \sim \triangle \mathrm{FDE}$
Hence the correct answer is $(a)$.