Question

two quadrilaterals are congruent. one has vertices p, n, o, and m, and the other has vertices s, t, v, and u. these corresponding congruent parts are known: • \\( \overline { o m } \cong \overline { t s } \\) • \\( \angle p \cong \angle u \\) which congruency statements could be correct for the figures? choose two correct answers. \\( \square \\) mnpo ( \cong ) tsvu \\( \square \\) npom ( \cong ) vuts \\( \square \\) mnop ( \cong ) stuv \\( \square \\) opnm ( \cong ) tuvs \\( \square \\) ponm ( \cong ) utsv

Explanation:

Step1: Analyze congruent parts

Given \(\overline{OM}\cong\overline{TS}\) and \(\angle P\cong\angle U\). In congruent quadrilaterals, the order of vertices must match corresponding parts.

Step2: Check each option

• For \(MNPO\cong TSVU\): The order does not match the given congruent parts (\(\overline{OM}\) and \(\overline{TS}\), \(\angle P\) and \(\angle U\)).
• For \(NPOM\cong VUTS\): The order does not match the given congruent parts.
• For \(MNOP\cong STUV\): The order does not match the given congruent parts.
• For \(OPNM\cong TUVS\): Here, \(O\) corresponds to \(T\), \(P\) corresponds to \(U\), \(N\) corresponds to \(V\), \(M\) corresponds to \(S\) which matches \(\overline{OM}\cong\overline{TS}\) (\(O - M\) and \(T - S\)) and \(\angle P\cong\angle U\).
• For \(PONM\cong UTSV\): Here, \(P\) corresponds to \(U\), \(O\) corresponds to \(T\), \(N\) corresponds to \(S\), \(M\) corresponds to \(V\) which does not match \(\overline{OM}\cong\overline{TS}\).

Answer:

\(NPOM\cong VUTS\), \(OPNM\cong TUVS\)