Question

in the figures below, the two triangles are similar.
a) which side in triangle xyz corresponds with np?
b) what is scale factor applied to \\(\triangle xyz\\) to achieve \\(\triangle mnp\\)? sf = (fraction)

Explanation:

Step1: Identify corresponding sides

Since the two triangles are similar, we match the sides. In similar triangles, corresponding sides are in proportion. Side \(NP\) in \(\triangle MNP\) corresponds to side \(YZ\) in \(\triangle XYZ\) because of the similarity of the triangles.

Step2: Calculate the scale factor

The scale factor \(SF\) is the ratio of the side lengths of the smaller triangle (\(\triangle MNP\)) to the larger triangle (\(\triangle XYZ\)). We use the pair of corresponding sides \(NP = 14\) and \(YZ=28\). The formula for scale factor is \(SF=\frac{\text{length of side in }\triangle MNP}{\text{length of corresponding side in }\triangle XYZ}\). So, \(SF = \frac{14}{28}\).
Simplifying \(\frac{14}{28}\), we divide both numerator and denominator by 14. \(\frac{14\div14}{28\div14}=\frac{1}{2}\)

Answer:

a) \(YZ\)
b) \(\frac{1}{2}\)