Answer:
C. No; you would need to know that each pair of diagonals is perpendicular.
Explanation:
It is not sufficient to establish that MNOP and TQRS are congruent parallelograms given that MO=TR and NP=QS. Parallelograms that are congruent have the same size and form. A common method for demonstrating that two parallelograms are congruent is to use one of the following criteria:
SSS (Side-Side-Side) : If all three pairs of corresponding sides are congruent.
SAS (Side-Angle-Side): If two pairs of corresponding sides and the included angle are congruent
ASA (Angle-Side-Angle): If two pairs of corresponding angles and the included side are congruent
HL (Hypotenuse-Leg): If the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle
CPCTC (Corresponding parts of Congruent Triangles are Congruent)
Given that we only know that MO=TR and NP=QS, we do not have enough information to prove that the parallelograms are congruent. It is missing information about the angles and the diagonals of the parallelograms.
In addition to that, we need to know that the diagonals of the parallelograms bisect each other. If this is the case, then we can use HL to prove that the parallelograms are congruent.