Question

which of the following statements are correct based on the diagram? select all that apply.

(overline{ut} cong overline{xv})

(angle s cong angle v)

(overline{st} cong overline{wv})

(angle v cong angle t)

(overline{us} cong overline{xv})

Explanation:

Step1: Analyze the triangles

We assume that \(\triangle SUT\) and \(\triangle XWV\) are congruent based on the markings (equal - side and equal - angle markings). If two triangles are congruent, their corresponding parts are congruent.

Step2: Check each option

• For \(\overline{UT}\cong\overline{XV}\): If \(\triangle SUT\cong\triangle XWV\), then \(UT\) (a side of \(\triangle SUT\)) and \(XV\) (a non - corresponding side of \(\triangle XWV\)) are not congruent.
• For \(\angle S\cong\angle V\): If \(\triangle SUT\cong\triangle XWV\), then \(\angle S\) (an angle of \(\triangle SUT\)) and \(\angle V\) (a non - corresponding angle of \(\triangle XWV\)) are not congruent.
• For \(\overline{ST}\cong\overline{WV}\): If \(\triangle SUT\cong\triangle XWV\), then \(ST\) (a side of \(\triangle SUT\)) and \(WV\) (a non - corresponding side of \(\triangle XWV\)) are not congruent.
• For \(\angle V\cong\angle T\): If \(\triangle SUT\cong\triangle XWV\), then \(\angle T\) (an angle of \(\triangle SUT\)) and \(\angle V\) (a non - corresponding angle of \(\triangle XWV\)) are not congruent.
• For \(\overline{US}\cong\overline{XV}\): If \(\triangle SUT\cong\triangle XWV\), then \(US\) (a side of \(\triangle SUT\)) and \(XV\) (a side of \(\triangle XWV\)) are congruent as corresponding parts.

Answer:

\(\overline{US}\cong\overline{XV}\)