Chapter 2, Problem 4RP

To determine

To Conclude: In the given figure $\overline{NG}\cong \overline{OH}$

Explanation of Solution

Given information : We are given $\overline{FG}\cong \overline{JH}\text{.}$

  $N$ is the mid-point of $\overline{FG}\text{, }O$ is the mid-point of $\overline{JH}$

Formula used : If two segments are congruent, then their like divisions are also congruent.

Proof: As per the given statement $\overline{FG}\cong \overline{JH}$ .Now as their whole are congruent so their halves also will be congruent thus

  $\frac{1}{2}\overline{FG}\cong \frac{1}{2}\overline{JH}\mathrm{...........................................................}\text{(i)}$

We have $N$ is the mid-point of $\overline{FG}$ ,it means $\overline{NG}\text{ =}\frac{1}{2}\overline{FG}\mathrm{.....................................}\text{(ii)}$

Also $O$ is the mid-point of $\overline{JH}$ ,it means $\overline{OH}\text{ =}\frac{1}{2}\overline{JH}\mathrm{.....................................}\text{(iii)}$

Taking values from (ii), (iii) and plugging it in (i) we get:

  $\begin{array}{l}\frac{1}{2}\overline{FG}\cong \frac{1}{2}\overline{JH}\\ \\ \Rightarrow \overline{NG}\cong \overline{OH}\end{array}$

Which proves the required result.