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

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Re: In the quadrilateral PQRS, side PS is parallel to side QR. [#permalink]
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Hi,

from both A & B each considered alone we can say that they can be rectangel, rhoumbus, IIogram or trapeizium. Hence INSUFFICIENT

Combining them also does not change the situation. HENCE INSUFFICIENT.

I would normally go for E and not A.

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Re: In the quadrilateral PQRS, side PS is parallel to side QR. [#permalink]
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So if 2 opp sides are equal means it is ||gram? not matter it is square or rohbus or rectangle?
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Re: In the quadrilateral PQRS, side PS is parallel to side QR. [#permalink]
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ssruthi wrote:
So if 2 opp sides are equal means it is ||gram? not matter it is square or rohbus or rectangle?

If two opposite sides are parallel and equal, then its definitely a parallelogram. It could be a square,rhombus or rectangle ( all are types of parallelogram)
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In the quadrilateral PQRS, side PS is parallel to side QR. Is PQRS a parallelogram?

(2) PQ = RS

I'm having a tough time seeing how this wouldn't be a parallelogram.

We know that a.) the figure has 4 sides and b.) that PS || PR. In addition, we are told that PQ=RS. I cannot construct a four sided figure with these constraints that doesn't have two pairs of parallel sides. Can someone please explain what I am missing and the logic behind how to solve these kinds of problems?
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WholeLottaLove wrote:
In the quadrilateral PQRS, side PS is parallel to side QR. Is PQRS a parallelogram?

(2) PQ = RS

I'm having a tough time seeing how this wouldn't be a parallelogram.

We know that a.) the figure has 4 sides and b.) that PS || PR. In addition, we are told that PQ=RS. I cannot construct a four sided figure with these constraints that doesn't have two pairs of parallel sides. Can someone please explain what I am missing and the logic behind how to solve these kinds of problems?

Refer to the image, where PQ=SR and PS || QR.
Attachments

image.png [ 2.95 KiB | Viewed 88497 times ]

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Good God I don't know how I missed that.
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In statement 1 couldn't figure be a rectangle? Is a rectangle a type of parallelogram? I guess so right?

Thanks
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In the quadrilateral PQRS, side PS is parallel to side QR. [#permalink]
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(basic) properties of a parallelogram:

a) opposite sides are parallel and of the same length

b) interior angles add up to 360 degrees

c) opposite angles are equal, and adjacent angles sum to 180

Knowing the above:

1) PS=QR. Given: PS//QR. Textbook definition of //gram. sufficient.

2) PQ=RS. Does not mention whether PQ//RS, whether PS=QR, etc. insufficient.

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Re: In the quadrilateral PQRS, side PS is parallel to side QR. [#permalink]
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Re: In the quadrilateral PQRS, side PS is parallel to side QR. [#permalink]
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