Chapter 9.3, Problem 22PSC

To determine

To Prove: The product of ratios of sides $JH\text{ and }GH,GH\text{ and }HF$ are equal, i.e., $\frac{JH}{GH}=\frac{GH}{HF}$

Explanation of Solution

Given information :

  $\begin{array}{l}\overline{FG}\perp \overline{GH}\\ \angle 1+\angle 3=90°\end{array}$

Formula used :

Ratios of corresponding sides are equivalent.

Proof :

In triangles $GJH$ and $FGJ$ , we have

  $\begin{array}{l}\angle 1=\angle \mathrm{2......}\text{Vertical angles}\\ \angle 3+\angle 4=90°\\ \angle 1+\angle 3=90°\\ \angle 1=\angle 4\end{array}$

Now.

  $\frac{JH}{GH}=\frac{GH}{HF}$

Hence proved