Question

Determine if the pair of triangles are similar.

Similarity
Determine if the pair of triangles are similar.

not similar
AA sim
SAS sim
SSS sim

2021-08-07
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.