Question

in the coordinate plane, plot $overline{ab}$ and $overline{cd}$ given by the points $a(-4,5)$, $b(-4,8)$, $c(2, - 3)$, $d(2,0)$. determine whether $overline{ab}$ and $overline{cd}$ are congruent.

Explanation:

Step1: Calculate length of $\overline{AB}$

Since $A(-4,5)$ and $B(-4,8)$ have the same $x$-coordinate, the length of $\overline{AB}$ is $|8 - 5|=3$.

Step2: Calculate length of $\overline{CD}$

Since $C(2,-3)$ and $D(2,0)$ have the same $x$-coordinate, the length of $\overline{CD}$ is $|0-(-3)| = 3$.

Step3: Compare lengths

Since the length of $\overline{AB}=3$ and the length of $\overline{CD}=3$, they are congruent.

Answer:

$\overline{AB}$ and $\overline{CD}$ are congruent.