Question

given: s is the mid - point of rt, u is the mid - point of vt, and rs≅vu. prove: st≅ut. step statement reason 1 s is the mid - point of rt given 2 u is the mid - point of vt given 3 rs≅vu given 4 rs = ut 5 st = ut

Explanation:

Step1: Recall mid - point property

Since \(S\) is the mid - point of \(\overline{RT}\), by the definition of a mid - point, \(RS = ST\).

Step2: Recall other given equalities

We know that \(RS\cong VU\) and \(U\) is the mid - point of \(\overline{VT}\), so \(VU = UT\).

Step3: Use transitive property

Since \(RS = ST\) and \(RS=VU\) and \(VU = UT\), we can conclude that \(ST=UT\), so \(\overline{ST}\cong\overline{UT}\).

Answer:

\(\overline{ST}\cong\overline{UT}\)