Question

in the diagram, \\( \frac { s q } { o m } = \frac { s r } { o n } = 4 \\).

to prove that the triangles are similar by the sss similarity theorem, which other sides or angles should be used?

\\( \bigcirc \overline { m n } \\) and \\( \overline { s r } \\)
\\( \bigcirc \overline { m n } \\) and \\( \overline { q r } \\)
\\( \bigcirc \angle s \cong \angle n \\)
\\( \bigcirc \angle s \cong \angle o \\)

Explanation:

Step1: Recall SSS similarity theorem

SSS similarity theorem states that if the ratios of the corresponding sides of two triangles are equal, then the triangles are similar.
We already have \(\frac{SQ}{OM}=\frac{SR}{ON} = 4\). We need to check the ratio of the third - pair of sides.

Step2: Calculate the ratio of \(MN\) and \(QR\)

Given \(MN = 12\) and \(QR=48\). Then \(\frac{QR}{MN}=\frac{48}{12}=4\)

Answer:

\(\overline{MN}\) and \(\overline{QR}\)