Chapter 8, Problem 9CR

To determine

To find: whether $\overline{AB}$ , $\overline{CD}$ are congruent and plot the coordinates.

Answer to Problem 9CR

It is non congruent.

Explanation of Solution

Given:

The points in the coordinate:

  $\text{A}\left(8,-4\right),B\left(3,-4\right),C\left(7,1\right)\text{ and }D\left(7,-3\right).$

Concept used:

Line segments are congruent if they have the same length. However, they need not be parallel. They can be at any angle or orientation on the plane. In the figure above, there are two congruent line segments. Note they are laying at different angles. If you drag any of the four endpoints, the other segment will change length to remain congruent with the one you are changing.

The symbol for congruence is  $\cong$ .

Also, recall that the symbol for a line segment is a bar over two letters, so the statement $AB\cong PQ$ is read as the line segment $AB$ is congruent to the line $PQ$ .

Calculation:

  

Using ruler postulate:

  $\begin{array}{l}AB=\left|8-3\right|=5.\\ CD=\left|-3-1\right|=\left|-4\right|=4.\end{array}$

Since, segments are not same therefore, Segments are not congruent.

Hence, it is non congruent.