Chapter 3, Problem 3RP

To determine

To prove : The congruency of $\overline{FG}$ with respect to $\overline{GH}$ .

Explanation of Solution

Given information :

Here, we have given a circle with center O and $\overline{OG}\perp \overline{GH}$

Construction: Join $\overline{OF}$ and $\overline{OH}$ .

Proof: As, $\overline{OG}\perp \overline{GH}$ ,

  $\Rightarrow \angle OGF\cong \angle OGH\cong 90°$

Now, In $\Delta OGF$ and $\Delta OGH$ ,

  $\angle OGF\cong \angle OGH$ (Proved above)

  $\overline{OF}\cong \overline{OH}$ (Radius of circle)

  $\overline{OG}\cong \overline{OG}$ (Common)

  $\Rightarrow \Delta OGF\cong \Delta OGH$ (By RHS Congruency Rule)

  $\therefore \overline{FG}\cong \overline{GH}$ (By Corresponding Part of Congruent Triangles)