Question

given: $overline{wt}congoverline{tu}$; $overline{ru}$ and $overline{sw}$ are medians of $\triangle wtu$. prove: $overline{ru}congoverline{sw}$ 7. click here to insert 8. $\triangle rwucong\triangle suw$ 9. $overline{ru}congoverline{sw}$ 7. click here to insert 8. click here to insert 9. click here to insert

Explanation:

Step1: Recall median property

Since $\overline{RU}$ and $\overline{SW}$ are medians of $\triangle WTU$, $RW = \frac{1}{2}WT$ and $SU=\frac{1}{2}TU$.

Step2: Use given equality

Given $\overline{WT}\cong\overline{TU}$, then $RW = SU$.

Step3: Consider common side

$WU$ is a common side for $\triangle RWU$ and $\triangle SUW$, so $WU=WU$.

Step4: Apply SSS - congruence

In $\triangle RWU$ and $\triangle SUW$, we have $RW = SU$, $WU = WU$ and since $\overline{WT}\cong\overline{TU}$, we can show that $\triangle RWU\cong\triangle SUW$ by the Side - Side - Side (SSS) congruence criterion.

Step5: Use congruent - triangle property

If $\triangle RWU\cong\triangle SUW$, then corresponding parts of congruent triangles are congruent. So $\overline{RU}\cong\overline{SW}$.

Answer:

The proof is completed by showing that $\triangle RWU\cong\triangle SUW$ using SSS and then using the property of corresponding parts of congruent triangles to get $\overline{RU}\cong\overline{SW}$.