Question

refer the figure. are $overline{vt}$ and $overline{su}$ congruent?

Explanation:

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

The coordinates of $V$ is $(- 2a,0)$ and of $T$ is $(3a,0)$. Using the distance formula for two - points on a number line (since they have the same $y$ - coordinate $y = 0$), the length of $\overline{VT}=\vert3a-(-2a)\vert=\vert3a + 2a\vert=5a$.

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

The coordinates of $S$ is $(0,4a)$ and of $U$ is $(0,-a)$. Using the distance formula for two - points on a number line (since they have the same $x$ - coordinate $x = 0$), the length of $\overline{SU}=\vert4a-(-a)\vert=\vert4a + a\vert=5a$.

Answer:

Yes