Question

given: $overline{wt}congoverline{tu}$; $overline{ru}$ and $overline{sw}$ are medians of $\triangle wtu$. prove: $overline{ru}congoverline{sw}$ 7. $\triangle rwucong\triangle suw$ 7. corresponding parts of congruent tri - angles are congruent (c.p.c.t.c.) 8. $\triangle rwucong\triangle suw$ 8. click here to insert 9. $overline{ru}congoverline{sw}$ 9. click here to insert

Explanation:

Step1: Recall median property

Since $\overline{RU}$ and $\overline{SW}$ are medians of $\triangle WTU$, they divide the opposite - sides into two equal parts.

Step2: Use congruent - triangle property

We are given $\triangle RWU\cong\triangle SUW$. By the Corresponding Parts of Congruent Triangles are Congruent (C.P.C.T.C.) property, if two triangles are congruent, then their corresponding sides are congruent.

Step3: Identify corresponding sides

In $\triangle RWU$ and $\triangle SUW$, $\overline{RU}$ and $\overline{SW}$ are corresponding sides.

Answer:

Since $\triangle RWU\cong\triangle SUW$, by C.P.C.T.C., $\overline{RU}\cong\overline{SW}$