Question

in the diagram, \\(\frac{sq}{om} = \frac{sr}{on} = 4\\). diagram: triangle (mno) with (mn = 12), (no = 8), (mo = 15); triangle (sqr) with (sq = 60), (sr = 32), (qr = 48). to prove that the triangles are similar by the sss similarity theorem, which other sides or angles should be used?

• \\(\overline{mn}\\) and \\(\overline{sr}\\)
• \\(\overline{mn}\\) and \\(\overline{qr}\\)
• \\(\angle s \cong \angle n\\)
• \\(\angle s \cong \angle o\\)

Explanation:

Step1: Recall SSS Similarity

SSS similarity needs all three sides in proportion. We know \(\frac{SQ}{OM} = \frac{SR}{ON}=4\). Now check the third pair.

Step2: Calculate Proportions

For \(\overline{MN}\) (length 12) and \(\overline{QR}\) (length 48): \(\frac{QR}{MN}=\frac{48}{12} = 4\). So all three sides (\(SQ/OM\), \(SR/ON\), \(QR/MN\)) are in ratio 4, satisfying SSS similarity. Other options don't fit SSS (angles are for SAS, or wrong sides).

Answer:

\(\overline{MN}\) and \(\overline{QR}\) (the option: \(\overline{MN}\) and \(\overline{QR}\))