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Is the quadrilateral a square?

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Is the quadrilateral a square? [#permalink] New post 11 Feb 2012, 13:08
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

74% (01:19) correct 26% (00:21) wrong based on 61 sessions
Attachment:
ABCD.png
ABCD.png [ 10.14 KiB | Viewed 1305 times ]
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?
[Reveal] Spoiler: OA

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Last edited by Bunuel on 11 Feb 2012, 13:49, edited 2 times in total.
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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 1301 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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Re: Is the quadrilateral a square? [#permalink] New post 25 May 2013, 03:41
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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] 05 Aug 2013, 22:08
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