Chapter 2.7, Problem 10PSB

To determine

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

Explanation of Solution

Given information : The following information has been given

  $\overrightarrow{VW}\cong \overrightarrow{RS}$

  $\overrightarrow{XY}\cong \overrightarrow{RS}$

Formula used : Linear addition of lines is used

Proof : Applying virtue of congruency in the given information, we can say that

  $\overrightarrow{XY}\cong \overrightarrow{VW}$

Now, we add $\overrightarrow{WX}$ on both the sides of the equation. Hence, we get

  $\overrightarrow{WX}+\overrightarrow{VW}\cong \overrightarrow{WX}+\overrightarrow{XY}$

Simplifying both sides linearly, we get

  $\overrightarrow{VX}\cong \overrightarrow{WY}$

Hence, the required congruency is proved