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Is quadrilateral ABCD a parallelogram? (1) AC = BD

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DHAR
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Is quadrilateral ABCD a parallelogram? (1) AC = BD [#permalink] New post   Updated on: 07 Mar 2023, 08:12
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A
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65% (hard)

Question Stats:

39% (00:57) correct 61% (01:00) wrong based on 331 sessions
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Is quadrilateral ABCD a parallelogram?

(1) AC = BD
(2) AC and BD bisect each other.
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Official Answer
B

Originally posted by DHAR on 30 Jul 2017, 22:25.
Last edited by Bunuel on 07 Mar 2023, 08:12, edited 2 times in total.
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deepudiscover
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Re: Is quadrilateral ABCD a parallelogram? (1) AC = BD [#permalink] New post   31 Jul 2017, 04:10
DH99 wrote:
Is quadrilateral ABCD a parallelogram?

Statement 1: AC=BD
Statement 2: AC and BD bisect each other.


I think the answer should be B.
Diagonal bisecting each other proves parallelogram by using SAS(Side, Angle, Side) congruency.
Experts please help chetan2u
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chetan2u
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Re: Is quadrilateral ABCD a parallelogram? (1) AC = BD [#permalink] New post   31 Jul 2017, 07:41
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deepudiscover wrote:
DH99 wrote:
Is quadrilateral ABCD a parallelogram?

Statement 1: AC=BD
Statement 2: AC and BD bisect each other.


I think the answer should be B.
Diagonal bisecting each other proves parallelogram by using SAS(Side, Angle, Side) congruency.
Experts please help chetan2u



Hi..

I agree with you. diagonals bisecting each other is a SUFFICIENT condition for a Quadrilateral to be a PARALLELOGRAM..
DH99, pl relook in the Q. either there is a typing error( something else instead of Quadrilateral) or OA is marked incorrectly.
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Re: Is quadrilateral ABCD a parallelogram? (1) AC = BD [#permalink] New post   31 Jul 2017, 08:04
It can be rhombus or square as well
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Re: Is quadrilateral ABCD a parallelogram? (1) AC = BD [#permalink] New post   31 Jul 2017, 08:15
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vivek2k70 wrote:
It can be rhombus or square as well



Hi...
parallelogram is the BASE form of all these..
rhombus, square or rectangle .. all of them are TYPES of PARALLELOGRAM..
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Re: Is quadrilateral ABCD a parallelogram? (1) AC = BD [#permalink] New post   31 Jul 2017, 08:17
chetan2u wrote:
deepudiscover wrote:
DH99 wrote:
Is quadrilateral ABCD a parallelogram?

Statement 1: AC=BD
Statement 2: AC and BD bisect each other.


I think the answer should be B.
Diagonal bisecting each other proves parallelogram by using SAS(Side, Angle, Side) congruency.
Experts please help chetan2u



Hi..

I agree with you. diagonals bisecting each other is a SUFFICIENT condition for a Quadrilateral to be a PARALLELOGRAM..
DH99, pl relook in the Q. either there is a typing error( something else instead of Quadrilateral) or OA is marked incorrectly.



Hi,

The OA is marked as E.This is how I solved it I am not sure if it is correct.Please evaluate:
Statement1>> Can be a Isoscelles Trapezium,Square/Rectangle.(Isoscelles Trapezium is a not a ||gm but a quadrilateral)
Statement1>> Can be a Isoscelles Trapezium, Square/Rectangle.

1+2>> Isoscelles Trapezium or Rectangle . E
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Re: Is quadrilateral ABCD a parallelogram? (1) AC = BD [#permalink] New post   31 Jul 2017, 08:38
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DH99 wrote:
chetan2u wrote:
deepudiscover wrote:

I think the answer should be B.
Diagonal bisecting each other proves parallelogram by using SAS(Side, Angle, Side) congruency.
Experts please help chetan2u



Hi..

I agree with you. diagonals bisecting each other is a SUFFICIENT condition for a Quadrilateral to be a PARALLELOGRAM..
DH99, pl relook in the Q. either there is a typing error( something else instead of Quadrilateral) or OA is marked incorrectly.



Hi,

The OA is marked as E.This is how I solved it I am not sure if it is correct.Please evaluate:
Statement1>> Can be a Isoscelles Trapezium,Square/Rectangle.(Isoscelles Trapezium is a not a ||gm but a quadrilateral)
Statement1>> Can be a Isoscelles Trapezium, Square/Rectangle.

1+2>> Isoscelles Trapezium or Rectangle . E


OA is wrong then. It has to be B
Isosceles trapezium - its diagonals do not bisect each other. they are equal.
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Re: Is quadrilateral ABCD a parallelogram? (1) AC = BD [#permalink] New post   01 Aug 2017, 10:08
Attachment:
quadrilateral.jpg
quadrilateral.jpg [ 41.35 KiB | Viewed 7705 times ]


It can also be in this shape.. here AC = BD and AC and BD bisects.. this is not a parallelogram.

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Re: Is quadrilateral ABCD a parallelogram? (1) AC = BD [#permalink] New post   01 Aug 2017, 10:22
imyuva wrote:
Attachment:
quadrilateral.jpg


It can also be in this shape.. here AC = BD and AC and BD bisects.. this is not a parallelogram.

Sent from my KIW-L22 using GMAT Club Forum mobile app


These diagonals will not bisect each other in this case. You can go ahead and draw an isosceles trapezium to scale and then measure to see if the diagonals bisect each other.. You will realize that they will not! Only in a parallelogram can this happen.
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Is quadrilateral ABCD a parallelogram? (1) AC = BD (2) AC and BD bise [#permalink] New post   01 Dec 2021, 04:58
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Property of a parallelogram: Diagonals of a parallelogram bisect each other. Statement 2 states that explicitly and thus is sufficient.
Statement 1 is insufficient as diagonals can be equal even in the case of a trapezium which is not a parallelogram, thus this condition alone is not sufficient.
Option (B).
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Re: Is quadrilateral ABCD a parallelogram? (1) AC = BD (2) AC and BD bise [#permalink] New post   17 Feb 2022, 07:40
Property of a parallelogram: Diagonals of a parallelogram bisect each other. - But this also is the property of the Rectangle?
And Rectangle is also a quadrilateral.
I think the answer is option E.
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Is quadrilateral ABCD a parallelogram? (1) AC = BD (2) AC and BD bise [#permalink] New post   14 Apr 2022, 06:46
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Asha7 wrote:
Property of a parallelogram: Diagonals of a parallelogram bisect each other. - But this also is the property of the Rectangle?
And Rectangle is also a quadrilateral.
I think the answer is option E.


Asha7

All rectangles are parallelograms.

Bunuel

I understand that difficulty level of a question is determined basis % of students who marks correctly. However, this is a property question and don't think should be classified as 700-level. There should be some more parameters to classify difficulty level of a ques.

gmatwhiz

Your concept file in FT states that diagonals of a trapezium are not equal. However, as per this ques OA, it seems that they may be equal.
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Quad with trapezium.png
Quad with trapezium.png [ 703.42 KiB | Viewed 2210 times ]

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Re: Is quadrilateral ABCD a parallelogram? (1) AC = BD [#permalink] New post   07 Jul 2023, 02:26
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Re: Is quadrilateral ABCD a parallelogram? (1) AC = BD [#permalink]
07 Jul 2023, 02:26
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Bunuel
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