Questions: L .3 proving triangles congruent by SSS and SAS WZ R is the midpoint of QS. Complete the proof that triangle RSU is congruent to triangle RQT. 1. R is the midpoint of QS - Given 2. QT is congruent to SU - Given 3. RT is congruent to RU - Given 4.

L .3 proving triangles congruent by SSS and SAS WZ
R is the midpoint of QS. Complete the proof that triangle RSU is congruent to triangle RQT.

1. R is the midpoint of QS - Given
2. QT is congruent to SU - Given
3. RT is congruent to RU - Given
4.
Transcript text: $L .3$ proving triangles congruent by SSS and SAS WZ $R$ is the midpoint of $\overline{Q S}$. Complete the proof that $\triangle R S U \cong \triangle R Q T$. \begin{tabular}{|l|l|l|} \hline & Statement & Reason \\ \hline 1 & $R$ is the midpoint of $\overline{Q S}$ & Given \\ 2 & $\overline{Q T} \cong \overline{S U}$ & Given \\ 3 & $\overline{R T} \cong \overline{R U}$ & Given \\ 4 & & \\ \hline & & \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Determine the congruent segments

Since $R$ is the midpoint of $\overline{QS}$, we know that $\overline{QR} \cong \overline{RS}$.

Step 2: Identify the congruent triangles

We are given that $\overline{QT} \cong \overline{SU}$ and $\overline{RT} \cong \overline{RU}$.

Step 3: Complete the proof

We have $\overline{QR} \cong \overline{RS}$, $\overline{QT} \cong \overline{SU}$, and $\overline{RT} \cong \overline{RU}$. Therefore, by Side-Side-Side (SSS) congruence, $\triangle RSU \cong \triangle RQT$.

Final Answer

\begin{tabular}{|l|l|l|} \hline & Statement & Reason \\ \hline 1 & $R$ is the midpoint of $\overline{Q S}$ & Given \\ 2 & $\overline{Q T} \cong \overline{S U}$ & Given \\ 3 & $\overline{R T} \cong \overline{R U}$ & Given \\ 4 & $\overline{Q R} \cong \overline{R S}$ & Definition of midpoint \\ 5 & $\triangle R S U \cong \triangle R Q T$ & SSS \\ \hline \end{tabular} \\(\boxed{\triangle RSU \cong \triangle RQT}\\)

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