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# In the quadrilateral PQRS, side PS is parallel to side QR.

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In the quadrilateral PQRS, side PS is parallel to side QR. [#permalink]  27 Oct 2007, 13:42
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In the quadrilateral PQRS, side PS is parallel to side QR. Is PQRS a parallelogram?

(1) PS = QR

(2) PQ = RS
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OG 11 - page 131

"A polygon with four sides is a quadrilateral in which both pairs of opposite sides are parallel is parallelogram.

The opposite sides of a parallelogram also have equal length".

quadrilateral PQRS can be a square.

Last edited by KillerSquirrel on 27 Oct 2007, 14:03, edited 1 time in total.
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jimjohn wrote:
can you plz explain why.

I have edited my post

VP
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jimjohn wrote:
the OA was A

Sorry I don't see it. Maybe someone else can ?

Manager
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heres what the explanation that i dont understand says:

------------------------------------------------------------------

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.

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jimjohn wrote:
heres what the explanation that i dont understand says:

------------------------------------------------------------------

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.

I still don't understand why PQRS cannot be a square.

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not sure if this helps but isnt a square just a type of parallelogram.
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From A we cannot say it is a square as it doesnt give any info about other two sides-PQ and SR being equal in length. but it is still not enough to say it is a parallellogram

only time when we make square is C only.
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jimjohn wrote:
not sure if this helps but isnt a square just a type of parallelogram.

Yes - just found it in the OG

when PS = QR and PS is parallel to side QR

then PQ & RS have to be equal & parallel when PQRS is a quadrilateral.

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# In the quadrilateral PQRS, side PS is parallel to side QR.

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