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{om}congoverline{ts})
(angle pcongangle u)
which congruency statements could be correct for the figures? check all that apply.
(square mnopcong stuv)
(square mnpocong tsvu)
(square npomcong vuts)
(square opnmcong tuvs)
(square ponmcong utsv)

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# Explanation:
## Step1: Analyze congruency statements based on given congruent parts
- For congruent quadrilaterals, the order of vertices in the congruency statement must match the corresponding congruent parts.
- Given $\overline{OM}\cong\overline{TS}$, so $O$ corresponds to $T$ and $M$ corresponds to $S$. Given $\angle P\cong\angle U$, so $P$ corresponds to $U$.
## Step2: Check each option
- **Option 1: $MNOP\cong STUV$**
  - Here, $M$ is first in $MNOP$ and $S$ is first in $STUV$ (from $\overline{OM}\cong\overline{TS}$, $M$ corresponds to $S$). But $N$ in $MNOP$ and $T$ in $STUV$  -  $N$ does not correspond to $T$ (since $O$ corresponds to $T$ from $\overline{OM}\cong\overline{TS}$). So this is incorrect.
- **Option 2: $MNPO\cong TSVU$**
  - $M$ corresponds to $S$ (from $\overline{OM}\cong\overline{TS}$), $N$ - no direct correspondence conflict yet. $P$ corresponds to $U$ (given $\angle P\cong\angle U$), $O$ corresponds to $T$ (from $\overline{OM}\cong\overline{TS}$). The order of vertices is correct as per the known congruent parts.
- **Option 3: $NPOM\cong VUTS$**
  - $N$ - no direct correspondence conflict. $P$ corresponds to $U$ (given $\angle P\cong\angle U$), $O$ corresponds to $T$ (from $\overline{OM}\cong\overline{TS}$), $M$ corresponds to $S$ (from $\overline{OM}\cong\overline{TS}$). The order of vertices is correct as per the known congruent parts.
- **Option 4: $OPNM\cong TUVS$**
  - $O$ corresponds to $T$ (from $\overline{OM}\cong\overline{TS}$), $P$ - no. Since $P$ should correspond to $U$ (given $\angle P\cong\angle U$), but in $TUVS$ there is no $U$ in the correct position. So this is incorrect.
- **Option 5: $PONM\cong UTSV$**
  - $P$ corresponds to $U$ (given $\angle P\cong\angle U$), $O$ corresponds to $T$ (from $\overline{OM}\cong\overline{TS}$), $N$ - no direct correspondence conflict, $M$ corresponds to $S$ (from $\overline{OM}\cong\overline{TS}$). The order of vertices is correct as per the known congruent parts.

# Answer:
MNPO ≅ TSVU, NPOM ≅ VUTS, PONM ≅ UTSV

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QUESTION IMAGE

Question

Explanation:

Step1: Analyze congruency statements based on given congruent parts

Step2: Check each option

Answer: