Chapter 8, Problem 22RP

To determine

To prove:The ratio of corresponding sides is equivalent.

Explanation of Solution

Given information:

Two lines are parallel, i.e., $\overleftrightarrow{\text{HR}}\parallel \overleftrightarrow{\text{GM}}$

Formula used:

Similarity of quadrilaterals

Proof:

In quadrilaterals RPOM and HGOP, we have

  $\overleftrightarrow{\text{HR}}\parallel \overleftrightarrow{\text{GM}}$ …….given

  $\therefore$ RP $\parallel$ OM and HP $\parallel$ GO

Thus,

Corresponding sides will be always in proportion

  $\frac{\text{RP}}{\text{OM}}=\frac{\text{HP}}{\text{GO}}$