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

Correct answers:
- NPOM ≅ VUTS
- OPNM ≅ TUVS

Reason: each congruence must send P to U and the segment OM to TS. For NPOM ≅ VUTS the mapping is N→V, P→U, O→T, M→S (so OM → TS). For OPNM ≅ TUVS the mapping is O→T, P→U, N→V, M→S (so OM → TS). The other lists either do not send P to U or do not send OM to TS.