Chapter 14, Problem 1PE

To determine

To prove: $\frac{PO}{RO}=\frac{PQ}{RS}$

Explanation of Solution

Given information:

  $\overline{PQ}\left|\right|\overline{RS}$ of the given figure.

  

Calculation:

From $\Delta SOR$ and $\Delta POR$ ,

  $\begin{array}{l}\angle OSR=\angle OQR\text{ (Alternative angles)}\\ \angle ORS=\angle OPQ\text{ (Alternative angles)}\end{array}$

Therefore formula $\Delta SOR$ and $\Delta POR$ are congruent. Which follows,

  $\begin{array}{l}\frac{RO}{QO}=\frac{SO}{PO}=\frac{SR}{PO}\\ \Rightarrow \frac{RO}{QO}=\frac{SO}{PO}\\ \Rightarrow \frac{PO}{RO}=\frac{PQ}{RS}\end{array}$

Hence proved.