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Senior Manager  Joined: 28 Jun 2007
Posts: 284
In the figure above, is quadrilateral PQRS a parallelogram?  [#permalink]

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1
11 00:00

Difficulty:   55% (hard)

Question Stats: 53% (01:19) correct 47% (01:13) wrong based on 212 sessions

### HideShow timer Statistics In the figure above, is quadrilateral PQRS a parallelogram?

(1) The area of ΔPQS is equal to the area of ΔQRS.
(2) QR = RS

Attachment: Q2.jpg [ 3.35 KiB | Viewed 19926 times ]

Originally posted by gluon on 12 Oct 2007, 12:07.
Last edited by Bunuel on 21 Jul 2015, 03:04, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Math Expert V
Joined: 02 Sep 2009
Posts: 53738
Re: In the figure above, is quadrilateral PQRS a parallelogram?  [#permalink]

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4
4
Is the quadrilateral PQRS a parallelogram where QS is the diagnol.

(1) The area of triangle PQS is equal to the area of triangle QRS.

Well yes: the area of a parallelogram is twice the area of a triangle created by one of its diagonals. But the opposite is not correct: two triangles can share the same base, have the same area BUT their two corresponding side not necessary to be parallel. --> Not sufficient.

(2) QR = RS. --> QRS is isosceles. For PQRS to be parallelogram QPS also must be isosceles, in this case we get rhombus, but it's OK every rhombus is parallelogram. But we don't know that. --> Not sufficient.

(1)+(2) Area QRS=Area PQS, QRS is isosceles. --> PQS can have the same area as QRS and not be isosceles. So not sufficient.

E.

Parallelogram is a quadrilateral with two sets of parallel sides.

The opposite or facing sides of a parallelogram are of equal length, and the opposite angles of a parallelogram are equal.

Opposite sides of a parallelogram are equal in length.

Opposite angles of a parallelogram are equal in measure.

The area of a parallelogram is twice the area of a triangle created by one of its diagonals.

The diagonals of a parallelogram bisect each other.

Every rhombus is a parallelogram. Opposite is not correct.

Every square is a parallelogram. Opposite is not correct.
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Manager  Joined: 07 Sep 2007
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Re: In the figure above, is quadrilateral PQRS a parallelogram?  [#permalink]

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gluon wrote:
In the figure above, is quadrilateral PQRS a parallelogram?
(1) The area of ΔPQS is equal to the area of ΔQRS.
(2) QR = RS

E

1 tells us nothing about angles or "parallelogramness"
2 tells us nothing about angles or "parallelogramness"

Together tells us nothing either.
Director  Joined: 09 Aug 2006
Posts: 721
Re: In the figure above, is quadrilateral PQRS a parallelogram?  [#permalink]

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1
E.

|| gram is a quadrilateral in which opp. sides are equal and parallel.

Stat 1:
Tells us nothing about the parallel sides; insuff.

Stat 2:
These are adjacent sides; insuff.

Stat 1 & 2:
Still doesn't provide us with any useful info.
Senior Manager  Joined: 30 Nov 2008
Posts: 466
Schools: Fuqua
Re: In the figure above, is quadrilateral PQRS a parallelogram?  [#permalink]

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Is the quadrilateral PQRS a parallelogram where QS is the diagnol.

(1) The area of triangle PQS is equal to the area of triangle QRS.
(2) QR = RS.

I guess it wrong. Just wanted to know whether I am missing any property of a quadrilateral for it to be a parallelogram. .

I am not sure whether OA is correct. But I will let you know the OA after some replies.

Originally posted by mrsmarthi on 22 Oct 2009, 12:06.
Last edited by Bunuel on 20 Jun 2013, 04:37, edited 1 time in total.
Math Expert V
Joined: 02 Sep 2009
Posts: 53738
In the figure above, is quadrilateral PQRS a parallelogram?  [#permalink]

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1
mrsmarthi wrote:
Is the quadrilateral PQRS a parallelogram where QS is the diagnol.

A) The area of triangle PQS is equal to the area of triangle QRS.
B) QR = RS.

I guess it wrong. Just wanted to know whether I am missing any property of a quadrilateral for it to be a parallelogram. .

I am not sure whether OA is correct. But I will let you know the OA after some replies.

Well my first thought is E. Or there is some catch I cannot notice...
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Senior Manager  Joined: 30 Nov 2008
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Re: In the figure above, is quadrilateral PQRS a parallelogram?  [#permalink]

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Bunuel,

Well I assumed that when the diagnol of the quadrilateral divedes it into two triangles of equal area, then the quadrilateral must be parallelogram. But I guess this assumption is wrong.

IN a parallelogram, the diagnols divide it into two triangles of equal areas but need NOT be true with quadrilateral.

OA is E.
Senior Manager  Joined: 30 Nov 2008
Posts: 466
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Re: In the figure above, is quadrilateral PQRS a parallelogram?  [#permalink]

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Bunuel,

Thank you for the detailed explanation.
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Re: In the figure above, is quadrilateral PQRS a parallelogram?  [#permalink]

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gluon wrote: In the figure above, is quadrilateral PQRS a parallelogram?

(1) The area of ΔPQS is equal to the area of ΔQRS.
(2) QR = RS

Attachment:
Q2.jpg

Statement 1: The area of ΔPQS is equal to the area of ΔQRS.

The figure may be a Parallelogram or a Kite shape figure (non-parallelogram). Hence,
NOT SUFFICIENT

Statement 2: QR = RS

The figure may be a Parallelogram or an Isosceles triangle above the Diagonal and an scalene triangle below the diagonal of quadrilateral (non-parallelogram). Hence,
NOT SUFFICIENT

Combining the two statements:
The figure may be a Parallelogram or an Isosceles triangle above the Diagonal and an scalene triangle below the diagonal of quadrilateral (non-parallelogram) such that area of both halves of the Quadrilateral are same. Hence,
NOT SUFFICIENT

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In the figure above, is quadrilateral PQRS a parallelogram?  [#permalink]

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gluon wrote: In the figure above, is quadrilateral PQRS a parallelogram?

(1) The area of ΔPQS is equal to the area of ΔQRS.
(2) QR = RS

Attachment:
Q2.jpg

hi

lets consider this logic:
area of a triangle = (1/2) * base * height

now

triangle, (1/2) * 3 * 4 and triangle, (1/2) * 4 * 3 have the same area, but

is it necessary that these two triangles are congruent ? Certainly no

on this line of reasoning, we can conclude that the the answer is straight "E"

please raise your voice if there is anything wrong here

thanks, and cheers with +1 Non-Human User Joined: 09 Sep 2013
Posts: 10151
Re: In the figure above, is quadrilateral PQRS a parallelogram?  [#permalink]

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_________________ Re: In the figure above, is quadrilateral PQRS a parallelogram?   [#permalink] 21 Feb 2019, 04:37
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# In the figure above, is quadrilateral PQRS a parallelogram?

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