Question

current skill $\triangle lvt\sim\triangle nbj$ which proportion shows the similarity between these two figures? $\frac{lv}{lt}=\frac{nb}{nj}$ $\frac{vl}{bn}=\frac{tl}{lv}$ $\frac{lv}{lt}=\frac{vl}{bn}$ $\frac{vl}{bn}=\frac{nj}{nb}$

Explanation:

Step1: Recall the property of similar triangles

For similar triangles \(\triangle LVT\sim\triangle NBJ\), the ratios of corresponding sides are equal. That is \(\frac{LV}{NB}=\frac{VT}{BJ}=\frac{LT}{NJ}\)

Step2: Rearrange the proportion

From \(\frac{LV}{NB}=\frac{LT}{NJ}\), we can cross - multiply to get \(LV\times NJ = NB\times LT\). Also, we know that by the property of proportion \(\frac{VL}{BN}=\frac{TL}{LV}\) (by re - arranging the ratio of corresponding sides of similar triangles. If \(\triangle LVT\sim\triangle NBJ\), then \(LV\) corresponds to \(NB\), \(VT\) corresponds to \(BJ\), \(LT\) corresponds to \(NJ\). And \(\frac{VL}{BN}=\frac{TL}{LV}\) can be derived from \(\frac{LV}{NB}=\frac{LT}{NJ}\) by taking reciprocals and re - arranging the order of sides considering the similarity of triangles)

Answer:

\(\frac{VL}{BN}=\frac{TL}{LV}\)