Chapter 2.7, Problem 6PSA

To determine

To prove : The congruency of $\overrightarrow{GH}\cong \overrightarrow{JK}$ is to be proved

Explanation of Solution

Given information : The following information has been given

  $\overrightarrow{GJ}\cong \overrightarrow{HK}$

Formula used : Linear addition of lines is used

Proof : Let us take the given equation

  $\overrightarrow{GJ}\cong \overrightarrow{HK}$

Now, we subtract $\overrightarrow{HJ}$ from both the sides

Hence, we now get

  $\overrightarrow{GJ}-\overrightarrow{HJ}\cong \overrightarrow{HK}-\overrightarrow{HJ}$

Simplifying both the sides of the equation, we get

  $\overrightarrow{GH}\cong \overrightarrow{JK}$

Hence, the given congruency has been proven