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Is the quadrilateral a square?
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enigma123
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Is the quadrilateral a square? [#permalink] New post  Updated on: 14 Sep 2019, 04:32
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ABCD.png
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Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA
(2) AC = BD

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In this question - How come the answer is C?

In Square the diagonals bisect each other at 90 degrees and are equal. How do we know that diagonals are bisecting each other at 90 degrees?
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Originally posted by enigma123 on 11 Feb 2012, 13:08.
Last edited by Bunuel on 14 Sep 2019, 04:32, edited 3 times in total.
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Bunuel
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Re: Is the quadrilateral a square? [#permalink] New post  11 Feb 2012, 13:48
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Attachment:
ABCD.png
ABCD.png [ 10.14 KiB | Viewed 8491 times ]
Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA --> both square and rhombus have all four sides equal in length. Not sufficient.

(2) AC = BD --> both square and rectangle have diagonals equal in length. Not sufficient.

(1)+(2) ABCD is a square. Sufficient.

Answer: C.

Useful property: if the diagonals of a rhombus are equal, then that rhombus must be a square. So you can apply this for (1)+(2) and conclude that ABCD must be a square.

Check Polygons chapter of Math Book for more useful properties and tips: math-polygons-87336.html

Hope it helps.
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madn800
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Re: Is the quadrilateral a square? [#permalink] New post  05 Aug 2013, 18:07
from 1 it is clear that it is either a rhombus or a square as all sides are equal.

from 2 it is established that it is a square as IN A RHOMBUS DIAGONALS ARE NOT EQUAL.

hence C.
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Re: Is the quadrilateral a square? [#permalink] New post  05 Aug 2013, 22:08
enigma123 wrote:
Attachment:
ABCD.png
Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA
(2) AC = BD

In this question - How come the answer is C?

In Square the diagonals bisect each other at 90 degrees and are equal. How do we know that diagonals are bisecting each other at 90 degrees?



square has equal sides and equal diagonals.
rhombus has equal sides but not equal diagonals.
so both together are sufficient...... Answer (C)

About the 2nd question, let p the point of intersection ofthe two diagonal AC and BD.
now angle PAB = angle PBA [because PA=PB]
so angle APB has to be 90 or it will not be possible for the total angle surrounding the point P to be 360.
so diagonals have to bisect at 90 degress
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Re: Is the quadrilateral a square? [#permalink] New post  24 Jul 2015, 01:23
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divyarathi15 wrote:
Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA
(2) AC = BD



Hi,
1) statement tells us all sides are equal. it could be a rhombus , a square etc.... insuff
2) stat 2 tells us that the diagonals are equal.. it could be a rectangle , a square or any other quad.. insuff

combined we know it can only be a square... suff
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divyarathi15
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Re: Is the quadrilateral a square? [#permalink] New post  24 Jul 2015, 01:32
Hi!

We could also say from statement 1 that it could be any irregular quadrilateral (apart from being either a rhombus/sq). Again from statement 2 it can be concluded that the figure could be any irregular quad too. combining both cant it be concluded that the figure could be an irregular quadrilateral too?
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Bunuel
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Re: Is the quadrilateral a square? [#permalink] New post  24 Jul 2015, 01:40
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divyarathi15 wrote:
Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA
(2) AC = BD


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Hope it helps.
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Re: Is the quadrilateral a square? [#permalink] New post  22 Jun 2017, 07:07
enigma123 wrote:
Attachment:
ABCD.png
Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA
(2) AC = BD

In this question - How come the answer is C?

In Square the diagonals bisect each other at 90 degrees and are equal. How do we know that diagonals are bisecting each other at 90 degrees?


Solution:

Statement 1: It can be either a square or rhombus. Insufficient.
Statement 2: It can be either a square or a parallelogram or a rectangle.

Combining St 1 and St 2, It has to be a square.

Therefore the answer is Option C.
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Re: Is the quadrilateral a square? [#permalink] New post  27 Jul 2017, 20:42
I did this question in the following method. Correct me if i am wrong . From the statement 1 the quadrilateral can be a Rhombus or a square. Hence not sufficient. Now from statement 2 the quadrilateral is a rhombus or a square or a rectangle.
1 and 2 together C
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Re: Is the quadrilateral a square? [#permalink] New post  27 Jul 2017, 20:47
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longhaul123 wrote:
I did this question in the following method. Correct me if i am wrong . From the statement 1 the quadrilateral can be a Rhombus or a square. Hence not sufficient. Now from statement 2 the quadrilateral is a rhombusor a square or a rectangle.
1 and 2 together C


A rhombus with equal diagonal is a square.
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Re: Is the quadrilateral a square? [#permalink] New post  14 May 2018, 06:06
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Statement 2: It can be either a square or a rectangle or any equidiagonal quadrilateral
Quadrilaterals with equal diagonal are called equidiagonal quadrilateral.
Attachment:
Equidiagonal Quandrilateral.jpg
Equidiagonal Quandrilateral.jpg [ 36.68 KiB | Viewed 4109 times ]



harikrish wrote:
enigma123 wrote:
Attachment:
The attachment ABCD.png is no longer available
Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA
(2) AC = BD

In this question - How come the answer is C?

In Square the diagonals bisect each other at 90 degrees and are equal. How do we know that diagonals are bisecting each other at 90 degrees?


Solution:

Statement 1: It can be either a square or rhombus. Insufficient.
Statement 2: It can be either a square or a parallelogram or a rectangle or any equidiagonal quadrilateral.

Combining St 1 and St 2, It has to be a square.

Therefore the answer is Option C.

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Re: Is the quadrilateral a square? [#permalink] New post  22 Aug 2019, 17:43
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