Question

3.11.1 prove it: parallel segments
now that we know the two triangles are similar, finish filling out
the ratios below that must be equivalent.
\\( \frac{am}{mb} = \frac{cn}{nb} \\)
\\( \frac{cb}{cn} = \frac{ab}{am} \\)
\\( \frac{ac}{\square} = \frac{mn}{\square} \\)

Explanation:

Step1: Recall the property of similar triangles

For similar triangles, the ratios of corresponding sides are equal.

Step2: Identify corresponding sides

Since \(\triangle ABC\sim\triangle MBN\) (by AA similarity as \(AC\parallel MN\), so \(\angle BAC=\angle BMN\) and \(\angle BCA = \angle BNM\)), the ratio \(\frac{AC}{MN}=\frac{AB}{MB}\)

Answer:

\(\frac{AC}{MN}=\frac{AB}{MB}\)