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), (qr = 48), (sr = 32).
to prove that the triangles are similar by the sss similarity theorem, which other sides or angles should be used?
(\bigcirc) (overline{mn}) and (overline{sr})
(\bigcirc) (overline{mn}) and (overline{qr})
(\bigcirc) (angle s cong angle n)
(\bigcirc) (angle s cong angle o)

Explanation:

To prove SSS similarity, all three corresponding sides must be in proportion. We know \(\frac{SQ}{OM} = \frac{SR}{ON}=4\). Now check \(\frac{QR}{MN}\): \(QR = 48\), \(MN = 12\), \(\frac{48}{12}=4\), so \(\overline{MN}\) and \(\overline{QR}\) make all sides proportional. Angles are for SAS/AA, not SSS. \(\overline{MN}\) and \(\overline{SR}\) don't correspond.

Answer:

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