Question

Determine if the pair of triangles are similar.

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asked 2021-08-06
Determine if the pair of triangles are similar.
image
not similar
AA sim
SAS sim
SSS sim

Answers (1)

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.
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