Question

use the given information to prove that $overline{st}congoverline{ut}$. given: $s$ is the midpoint of $overline{rt}$, $u$ is the midpoint of $overline{vt}$, and $overline{rs}congoverline{vu}$. prove: $overline{st}congoverline{ut}$ step statement reason 1 $s$ is the midpoint of $overline{rt}$, $u$ is the midpoint of $overline{vt}$ given 2 $overline{rs}congsquare$, $overline{vu}congsquare$ definition of midpoint 3 $overline{rs}congoverline{vu}$ given 4 $overline{rs}congoverline{ut}$ reason? 5 $overline{st}congoverline{ut}$ reason?

Explanation:

Step1: Apply mid - point definition for RS and ST

Since S is the mid - point of $\overline{RT}$, by the definition of mid - point, $\overline{RS}\cong\overline{ST}$.

Step2: Apply mid - point definition for VU and UT

Since U is the mid - point of $\overline{VT}$, by the definition of mid - point, $\overline{VU}\cong\overline{UT}$.

Step3: Use the given congruence

Given that $\overline{RS}\cong\overline{VU}$.

Step4: Use transitive property of congruence

Since $\overline{RS}\cong\overline{ST}$, $\overline{VU}\cong\overline{UT}$ and $\overline{RS}\cong\overline{VU}$, by the transitive property of congruence, $\overline{ST}\cong\overline{UT}$.

Answer:

$\overline{ST}\cong\overline{UT}$