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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]

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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
[Reveal] Spoiler: OA

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

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New post 29 Jun 2011, 04:10
Hi,

Can someone please explain the answer A?

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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New post 29 Jun 2011, 06:04
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well Option A says PS = QR and according to the question PS ll QR ...

hence PQ has to be equal and parallel to RS ....since connecting two equal and ll lines.

Otherwise the easiest way to find out whether it is a parallelogram or not draw two lines parallel and equal to each other and connect them with other two lines and see it will form a parallelogram

Therefore, this option is sufficient
Attachment:
2.jpg
2.jpg [ 24.01 KiB | Viewed 30557 times ]


Option B tells us that PQ = RS
Now, it does not tell us anything about PS and QR ... they can be unequal ... hence this option is insufficient to answer
Attachment:
3.jpg
3.jpg [ 20.34 KiB | Viewed 30565 times ]


Hence answer option A

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

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New post 07 Sep 2011, 07:11
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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New post 07 Sep 2011, 07:47
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 [#permalink]

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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


could you please share with ur thoughts on this?
and how to distinguish a square from a parallelogram in such a task?

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

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New post 01 May 2012, 10:17
Galiya wrote:
In the quadrilateral PQRS, side PS is parallel to side QR. Is PQRS a parallelogram?

(1) PS = QR

(2) PQ = RS


could you please share with ur thoughts on this?
and how to distinguish a square from a parallelogram in such a task?



If opposite sides of any quadrilateral are equal then its a parallelogram.But here only a is enough to determine that PQRS is a parallelogram.Bcoz PS=QR implies PQ=RS.But PQ=RS need not imply PS=QR(the isosceles trapezium).

We can't determine even using both 1 & 2 that PQRS is a square.

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

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New post 01 May 2012, 12:22
but square also has equal and parallel sides - i went with E since couldn't determine whether a square or a parallelogram in front of me

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

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New post 01 May 2012, 12:32
Galiya wrote:
but square also has equal and parallel sides - i went with E since couldn't determine whether a square or a parallelogram in front of me


That is correct, but not all parallelogram are squares.

Just because the sides are the same does not make it a square. If you were given an angle, which would have to be 90 degrees, that would make it a square.

What I do is make a parallelogram with angles that are not all 90 degrees on my paper until I can prove that it is a square. If you do it that way you should not have a problem again.
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Re: In the quadrilateral PQRS, side PS is parallel [#permalink]

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Galiya wrote:
but square also has equal and parallel sides - i went with E since couldn't determine whether a square or a parallelogram in front of me



:-D Square is also a Parallelogram.
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Re: In the quadrilateral PQRS, side PS is parallel [#permalink]

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New post 06 Dec 2013, 09:14
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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Re: In the quadrilateral PQRS, side PS is parallel [#permalink]

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

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Good God I don't know how I missed that. :shock:

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

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New post 16 May 2014, 09:52
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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J :)

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

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jlgdr wrote:
In statement 1 couldn't figure be a rectangle? Is a rectangle a type of parallelogram? I guess so right?

Thanks
Cheers
J :)


Hi J,
You are Right. :)
Actually, the statement 1 could well yield
a simple parallelogram or a rectangle or a rhombus or a square.

All these are types of parallelogram:
Simple parallelogram - a quadrilateral with opposite sides equal and parallel
Rectangle - a parallelogram with adjacent sides at 90 degrees
Rhombus - a parallelogram with all sides equal
Square - a parallelogram with adjacent sides at 90 degrees and all sides equal

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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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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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New post 04 Sep 2017, 16:22
(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.

--> A

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Re: In the quadrilateral PQRS, side PS is parallel to side QR.   [#permalink] 04 Sep 2017, 16:22
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