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Ok, here is the question. The information given in the question, PS and QR are parallel and the answer n* 1 (PS=QR), don't seem to define strictly a parallelogram .In other words, would a square still have 2 parallel sides that are also equal?
In the quadrilateral PQRS, side PS is parallel to side QR. Is PQRS a parallelogram?
(1) PS = QR
(2) PQ = RS
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. The opposite sides of a parallelogram also have equal length.
(1) SUFFICIENT: We know from the question stem that opposite sides PS and QR are parallel, while this statement tells us that they also have equal lengths. The opposite sides PQ and RS must also be parallel and equal in length. This is the definition of a parallelogram, so the answer to the question is "Yes."
(2) INSUFFICIENT: We know from the question stem that opposite sides PS and QR are parallel, but have no information about their respective lengths. This statement tells us that the opposite sides PQ and RS are equal in length, but we don’t know their respective angles; they might be parallel, or they might not be. According to the information given, PQRS could be a trapezoid with PS not equal to QR. On the other hand, PQRS could be a parallelogram with PS = QR. The answer to the question is uncertain.
The correct answer is A.