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Is quadrilateral ABCD a parallelogram ?

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Is quadrilateral ABCD a parallelogram ? [#permalink]

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Is quadrilateral ABCD a parallelogram ?

1) Two sides measure 8 cm in length while the other two sides measure 6 cm in length.

2) AC is perpendicular to BD.
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Re: Is quadrilateral ABCD a parallelogram ? [#permalink]

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New post 26 Aug 2013, 08:46
I think answer should be E. What if it is a kite type of shape. Then it is not a parallelogram but still meets the both criteria. I would wait for experts to comment..

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Re: Is quadrilateral ABCD a parallelogram ? [#permalink]

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AMITAGARWAL2 wrote:
I think answer should be E. What if it is a kite type of shape. Then it is not a parallelogram but still meets the both criteria. I would wait for experts to comment..


IMO as u say mate kite meets both the criterion and it is not a parallelogram therefore we are getting a definite answer
to with combining as "C" ...by combining the two information we are getting definite answer as NO "it is not a parallelogram" because it will be a kite which is NOT a parallelogram...

plz give kudos if it was a help..

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Re: Is quadrilateral ABCD a parallelogram ? [#permalink]

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New post 26 Aug 2013, 12:15
but with the current information it could be a rectangle, which is a rectangle and rectangle is a parallogram too. right? :(

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Re: Is quadrilateral ABCD a parallelogram ? [#permalink]

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AMITAGARWAL2 wrote:
but with the current information it could be a rectangle, which is a rectangle and rectangle is a parallogram too. right? :(


diagonals of RECTANGLE are not perpedicular,so in this case it cannot be rectangle.

diagonals are perpendicular only for SQUARE/RHOMBUS/KITE.

hope it helps
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Re: Is quadrilateral ABCD a parallelogram ? [#permalink]

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Statement 1 leads us to a parallelogram or a rectangle in which opposite sides are equal or to a Kite in which adjacent sides are equal ..thus all these quadrilaterals meet the criteria of st 1...Thus as we cant get a definite shape its insufficient..


Statement 2 leads us to a square , a rhombus or a kite....as diagonals of these three shapes intersect at right angle...so again no definite data and its insufficient..

Combining these two we can clearly infer that the figure is a kite ...OR its not a parallelogram for sure ....So we are getting a definite answer combining two statements ..Thus C...

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Re: Is quadrilateral ABCD a parallelogram ? [#permalink]

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New post 27 Aug 2013, 11:36
Thanks everyone... :)

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Re: Is quadrilateral ABCD a parallelogram ? [#permalink]

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Re: Is quadrilateral ABCD a parallelogram ? [#permalink]

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New post 30 Jul 2017, 17:15
Hello from the GMAT Club BumpBot!

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Re: Is quadrilateral ABCD a parallelogram ? [#permalink]

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New post 30 Jul 2017, 17:20
can someone please elaborate why a parallelogram does not fit both 1 & 2? I understand the kite part, but have a little confusion on the other.

Thanks!

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Re: Is quadrilateral ABCD a parallelogram ? [#permalink]

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New post 30 Jul 2017, 23:36
why cannot the answer be B

Statement 2 says that the diagonals are perpendicular, which means the figure can either be a square/rhombus/kite. This confirms that it is NOT A PARALLELOGRAM. A definite answer.

Have I missed something?

Thanks.

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Re: Is quadrilateral ABCD a parallelogram ? [#permalink]

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New post 04 Aug 2017, 09:54
AbhinavBankhwal wrote:
why cannot the answer be B

Statement 2 says that the diagonals are perpendicular, which means the figure can either be a square/rhombus/kite. This confirms that it is NOT A PARALLELOGRAM. A definite answer.

Have I missed something?

Thanks.


I agree! The answer should be B.

chetan2u and Bunuel could you please help us out with this question? :)
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Re: Is quadrilateral ABCD a parallelogram ? [#permalink]

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New post 05 Aug 2017, 13:28
rekhabishop wrote:
AbhinavBankhwal wrote:
why cannot the answer be B

Statement 2 says that the diagonals are perpendicular, which means the figure can either be a square/rhombus/kite. This confirms that it is NOT A PARALLELOGRAM. A definite answer.

Have I missed something?

Thanks.


I agree! The answer should be B.

chetan2u and Bunuel could you please help us out with this question? :)


Every square and Rhombus is a parallelogram


A parallelogram is a quadrilateral with 2 pairs of parallel sides.
The opposite sides on every square and on every rhombus are parallel, so every square and rhombus is a parallelogram.

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Re: Is quadrilateral ABCD a parallelogram ? [#permalink]

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innocous wrote:
Is quadrilateral ABCD a parallelogram ?

1) Two sides measure 8 cm in length while the other two sides measure 6 cm in length.

2) AC is perpendicular to BD.


Statement 1:

Image

Statement 2:

Image

Statements 1 and 2 together:

This is where it gets really interesting. We know the diagonals are perpendicular, and the four sides are 8, 8, 6, and 6.

There are only two possible ways to arrange the sides. Either the opposite sides are equal, like this:

Image

Or the adjacent sides are equal, like this:

Image

However, if the opposite sides are equal, the two diagonals can't be perpendicular.

Here's the simplest argument I could come up with to demonstrate that:

Image

The diagonals of a parallelogram should split each other in half. If they're perpendicular (have a right angle between them), we should be able to use right triangle rules! So, x^2 + y^2 = 6^2. However, we also have x^2 + y^2 = 8^2. It's impossible for the same equation to have two different values like that - so, it's logically impossible for the diagonals to be perpendicular.

In other words, if the opposite sides are equal, Statement 2 can't also be true. It's mathematically impossible. But Statement 2 has to be true, since we're combining the two statements together.

The only possible way to combine the two statements together and have them both be true, is if the adjacent sides are equal. This shape is the only possible one that fits both statements:

Image

This shape is not a parallelogram. So, we can definitively answer 'no' to the question. The correct answer is C.
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Re: Is quadrilateral ABCD a parallelogram ? [#permalink]

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New post 07 Sep 2017, 20:31
innocous wrote:
Is quadrilateral ABCD a parallelogram ?

1) Two sides measure 8 cm in length while the other two sides measure 6 cm in length.

2) AC is perpendicular to BD.


ccooley and Bunuel

This question https://gmatclub.com/forum/is-abcd-a-ro ... l#p1921432

States that if we know that a quadrilatral has perpendicular bisectors, two diagonals that bisect at 90, the we have enough to know that the figure is a rhombus? And if we know that the figure is a rhombus then we also know that the figure is a paralleogram? Kudos for explanation.

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Re: Is quadrilateral ABCD a parallelogram ? [#permalink]

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New post 07 Sep 2017, 20:35
innocous wrote:
Is quadrilateral ABCD a parallelogram ?

1) Two sides measure 8 cm in length while the other two sides measure 6 cm in length.

2) AC is perpendicular to BD.


ccooley https://gmatclub.com/forum/is-quadrilat ... 85336.html

This question also states that if we know that the diagonals of a quadrilateral are perpendicular bisectors of each other then we know for sure that the figure is a rhombus? And because a parallelogram is a broader category then wouldn't the figure have to be a parallelogram? What is the difference between the diagonals of a four sided figure being perpendicular to each other vs being perpendicular bisectors? Kudos

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Re: Is quadrilateral ABCD a parallelogram ? [#permalink]

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New post 07 Sep 2017, 20:39
Nunuboy1994 wrote:
innocous wrote:
Is quadrilateral ABCD a parallelogram ?

1) Two sides measure 8 cm in length while the other two sides measure 6 cm in length.

2) AC is perpendicular to BD.


ccooley https://gmatclub.com/forum/is-quadrilat ... 85336.html

This question also states that if we know that the diagonals of a quadrilateral are perpendicular bisectors of each other then we know for sure that the figure is a rhombus? And because a parallelogram is a broader category then wouldn't the figure have to be a parallelogram? What is the difference between the diagonals of a four sided figure being perpendicular to each other vs being perpendicular bisectors? Kudos


ccooley and Bunuel https://gmatclub.com/forum/is-quadrilat ... 45937.html

This question too- could please explain the difference between simply perpendicular diagonals and diagonals that are perpendicular bisectors?

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Is quadrilateral ABCD a parallelogram ? [#permalink]

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New post 07 Sep 2017, 21:28
Nunuboy1994 wrote:
Nunuboy1994 wrote:
innocous wrote:
Is quadrilateral ABCD a parallelogram ?

1) Two sides measure 8 cm in length while the other two sides measure 6 cm in length.

2) AC is perpendicular to BD.


ccooley https://gmatclub.com/forum/is-quadrilat ... 85336.html

This question also states that if we know that the diagonals of a quadrilateral are perpendicular bisectors of each other then we know for sure that the figure is a rhombus? And because a parallelogram is a broader category then wouldn't the figure have to be a parallelogram? What is the difference between the diagonals of a four sided figure being perpendicular to each other vs being perpendicular bisectors? Kudos


ccooley and Bunuel https://gmatclub.com/forum/is-quadrilat ... 45937.html

This question too- could please explain the difference between simply perpendicular diagonals and diagonals that are perpendicular bisectors?


A perpendicular bisector is a line which cuts a line segment into two equal parts at 90°.

A line segment bisector is a line which cuts a line segment into two equal parts.

A line is perpendicular to another if it meets or crosses it at right angles (90°).
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