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: OM ≅ TS ∠P ≅ ∠U Which congruency statements could be correct for the figures? Check all that apply. MNOP ≅ STUV MNPO ≅ TSVU NPOM ≅ VUTS OPNM ≅ TUVS PONM ≅ UTSV

Answer 1

The correct answers for this question are:

NPOM ≅ VUTS

OPNM ≅ TUVS

Answer 2

Answer: $NPOM \cong VUTS$ and $OPNM \cong TVUS$ will be correct.

Explanation:

Given: two quadrilaterals having verticals P, N, O,M and S,T,V,U are congruent,  where, OM is congruent or equal to TS and $\angle P\cong \angle U$.

in quadrilaterals NPOM and  VUTS-

since, the condition $\angle P = \angle U$

and, side UV=side  OM   follow for the above quadrilateral. (According to the figure)

then we can say according to the property of quadrilateral, their corresponding sides must be congruent. so they are congruent.

similarly, these two conditions also follow in the case of $OPNM \cong TVUS$

we can understand it by making the figures.