Questions: R is the midpoint of QS. Complete the proof that triangle RSU is congruent to triangle QRT. - Statement - Reason 1. R is the midpoint of QS - Given 2. SU is congruent to RT - Given 3. RU is congruent to QT - Given 4. QR is congruent to RS - Definition of midpoint 5. triangle RSU is congruent to triangle QRT -

R is the midpoint of QS. Complete the proof that triangle RSU is congruent to triangle QRT.

- Statement - Reason
1. R is the midpoint of QS - Given
2. SU is congruent to RT - Given
3. RU is congruent to QT - Given
4. QR is congruent to RS - Definition of midpoint
5. triangle RSU is congruent to triangle QRT -

Transcript text: $R$ is the midpoint of $\overline{Q S}$. Complete the proof that $\triangle R S U \cong \triangle Q R T$. \begin{tabular}{|l|l|l|} \hline & Statement & Reason \\ \hline 1 & $R$ is the midpoint of $\overline{Q S}$ & Given \\ 2 & $\overline{S U} \cong \overline{R T}$ & Given \\ 3 & $\overline{R U} \cong \overline{Q T}$ & Given \\ 4 & $\overline{Q R} \cong \overline{R S}$ & Definition of midpoint \\ 5 & $\triangle R S U \cong \triangle Q R T$ & \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Analyze given information

We are given that $R$ is the midpoint of $\overline{QS}$. This implies that $\overline{QR} \cong \overline{RS}$. We are also given that $\overline{SU} \cong \overline{RT}$ and $\overline{RU} \cong \overline{QT}$.

Step 2: Identify congruent triangles

We want to prove that $\triangle RSU \cong \triangle QRT$.

Step 3: Determine the congruence postulate

We have three pairs of congruent sides: \begin{itemize} \item $\overline{RS} \cong \overline{QR}$ \item $\overline{SU} \cong \overline{RT}$ \item $\overline{RU} \cong \overline{QT}$ \end{itemize} These three pairs of congruent sides correspond to the Side-Side-Side (SSS) congruence postulate.