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.