From the figure we can write as following:

\(\displaystyle{\frac{{{E}{F}}}{{{A}{B}}}}={\frac{{{42}}}{{{35}}}}={1.2}\)...(1)

\(\displaystyle{\frac{{{E}{D}}}{{{C}{B}}}}={\frac{{{30}}}{{{25}}}}={1.2}\)...(2)

\(\displaystyle{\frac{{{F}{D}}}{{{C}{A}}}}={\frac{{{24}}}{{{20}}}}={1.2}\)...(3)

From the equations (1), (2) and (3),

\(\displaystyle{\frac{{{E}{F}}}{{{A}{B}}}}={\frac{{{E}{D}}}{{{C}{B}}}}={\frac{{{F}{D}}}{{{C}{A}}}}\)

Since, the corresponding sides of the triangles are in same proportion. So, according to SSS similarity criteria. the triangle BCA \(\displaystyle\sim\) triangle EDF.

\(\displaystyle{\frac{{{E}{F}}}{{{A}{B}}}}={\frac{{{42}}}{{{35}}}}={1.2}\)...(1)

\(\displaystyle{\frac{{{E}{D}}}{{{C}{B}}}}={\frac{{{30}}}{{{25}}}}={1.2}\)...(2)

\(\displaystyle{\frac{{{F}{D}}}{{{C}{A}}}}={\frac{{{24}}}{{{20}}}}={1.2}\)...(3)

From the equations (1), (2) and (3),

\(\displaystyle{\frac{{{E}{F}}}{{{A}{B}}}}={\frac{{{E}{D}}}{{{C}{B}}}}={\frac{{{F}{D}}}{{{C}{A}}}}\)

Since, the corresponding sides of the triangles are in same proportion. So, according to SSS similarity criteria. the triangle BCA \(\displaystyle\sim\) triangle EDF.