Solution:
(c) BC · DE = AB · EF
Explanation:
We all know that,
If the sides of one triangle are proportionate to the sides of the other triangle, and the corresponding angles are all equal, the triangles are similar using SSS similarity criterion.
As a result, ∆ABC ∼ ∆EDF
Now using the similarity property,
AC/EF = AB/ED = BC/DF
Now taking AB/ED = BC/DF, we obtain
BC/DF = AB/ED
ED.BC = AB.DF
As a result, option (d) i.e., BC · DE = AB · FD is true
Now taking BC/DF = AC/EF, we get
AC/EF = BC/DF
⇒ AC.DF = BC.EF
As a result, option (a) i.e., BC · EF = AC · FD is true
Now taking AB/ED = AC/EF, we get,
AC/EF = AB/ED
ED.AC = AB.EF
As a result, option (b) i.e., AB · EF = AC · DE is true.