Question

select the proportion that relates the corresponding sides.
a) \\( \frac { m p } { q r } = \frac { m n } { r p } = \frac { n p } { q p } \\)
b) \\( \frac { n p } { q r } = \frac { m p } { r p } = \frac { m n } { q p } \\)
c) \\( \frac { m n } { q r } = \frac { m n } { r p } = \frac { m n } { q p } \\)
d) \\( \frac { m n } { q r } = \frac { n p } { r p } = \frac { m p } { q p } \\)
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Explanation:

Step1: Recall the concept of similar triangles

If two triangles are similar, the ratios of their corresponding sides are equal.

Step2: Identify corresponding sides

Assume \(\triangle QRP\sim\triangle MNP\) (based on the proportion context). The corresponding sides are \(QR\) and \(MN\), \(RP\) and \(NP\), \(QP\) and \(MP\).
The proportion of corresponding sides should be \(\frac{QR}{MN}=\frac{RP}{NP}=\frac{QP}{MP}\)

Answer:

A. \(\frac{QR}{MN}=\frac{RP}{NP}=\frac{QP}{MP}\)