Chapter 4, Problem 16CR

To determine

Prove $\overline{GH}\cong \overline{KJ}$

Explanation of Solution

Given:

  

  $\overline{GH}\perp \overline{HJ}$

  $\overline{KJ}\perp \overline{HJ}$

  $\overline{GJ}\cong \overline{KH}$

Calculation:

Consider the right angled $\Delta GHJ\text{ and }\Delta KJH$ :

  $\overline{GJ}\cong \overline{KH}$ , which are hypotenuse

  $\overline{HJ}\cong \overline{JH}$ , which are legs

So, by HL Postulate, $\Delta GHJ\cong \Delta KJH$ .

So, $\overline{GH}\cong \overline{KJ}$ .

Hence proved.