Question

the drawing below shows that the two triangles are similar. write the corresponding sides as equal ratios.
\\( \frac { m n } { b j } = \frac { n r } { j l } = \frac { r m } { m n } \\)
\\( \frac { m n } { b l } = \frac { n r } { l j } = \frac { r m } { j b } \\)
\\( \frac { m n } { b j } = \frac { n r } { j l } = \frac { r m } { l b } \\)
\\( \frac { l b } { b j } = \frac { n r } { j l } = \frac { r m } { m n } \\)

Explanation:

Step1: Identify corresponding sides

For similar triangles, corresponding sides are in proportion.

Step2: Match sides

In the given similar triangles, \(MN\) corresponds to \(BJ\), \(NR\) corresponds to \(JL\), and \(RM\) corresponds to \(LB\).

Step3: Write ratio

So the ratio of corresponding sides is \(\frac{MN}{BJ}=\frac{NR}{JL}=\frac{RM}{LB}\)

Answer:

\(\frac{MN}{BJ}=\frac{NR}{JL}=\frac{RM}{LB}\)