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# Is quadrilateral ABCD a rectangle?

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Manager
Joined: 17 Nov 2009
Posts: 219

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09 Sep 2010, 06:42
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Difficulty:

25% (medium)

Question Stats:

66% (00:48) correct 34% (01:00) wrong based on 342 sessions

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(1) Angle ABC = 90 degrees
(2) AB = CD
Senior Manager
Joined: 06 Jun 2009
Posts: 283
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09 Sep 2010, 06:59
agnok wrote:

1. angle ABC = 90 degrees
2. AB=CD

E

1. ABC = 90 ................ other angles can be of any value.

2. AB = CD ............... AC and BD might not be equal.

For rectangle, all angles have to be equal (hence, 90) and opposite sides should be equal. Neither of the two statement helps in determining if the two requirements are satisfied or not.
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Manager
Joined: 20 Jul 2010
Posts: 213

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09 Sep 2010, 07:08
E

for rectangle = all have to be 90 and opp sides equal
1. ABC= 90 : dont know about other angles - insuff
2. AB= CD , other sides may or may not be equal - insuff

together - not necessarily a rectangle, may be a square - insuff
Ans is E
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Math Expert
Joined: 02 Sep 2009
Posts: 52182

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09 Sep 2010, 08:02
1
2
agnok wrote:

1. angle ABC = 90 degrees
2. AB=CD

A rectangle is a quadrilateral with four right angles - this is necessary and sufficient condition for quadrilateral to be a rectangle.

(1) angle ABC = 90 degrees --> we know nothing about other angles. Not sufficient.
(2) AB=CD --> opposite sides AB and CD are equal, clearly insufficient.

(1)+(2) Look at the diagram:
Attachment:

rectangle.PNG [ 4.39 KiB | Viewed 7309 times ]
It's possible quadrilateral to be a rectangle (case ABCD1) and it's also possible quadrilateral not to be a rectangle (case ABCD2). Not sufficient.

saxenashobhit wrote:
E

for rectangle = all have to be 90 and opp sides equal
1. ABC= 90 : dont know about other angles - insuff
2. AB= CD , other sides may or may not be equal - insuff

together - not necessarily a rectangle, may be a square - insuff
Ans is E

metallicafan wrote:
E

It may be a square.

It's not necessary ABCD to be square (look at the diagram, it can be simple rectangle). In fact if we knew that ABCD is a square then statements would be sufficient, because square is a special type of rectangle, which means that every square is a rectangle (but not vise-versa).

Hope it helps.
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09 Sep 2010, 11:07
Manager
Joined: 20 Jul 2010
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12 Sep 2010, 08:59
Thanks Bunuel for the diagram
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18 Apr 2014, 03:02
Bunuel wrote:
agnok wrote:

1. angle ABC = 90 degrees
2. AB=CD

A rectangle is a quadrilateral with four right angles - this is necessary and sufficient condition for quadrilateral to be a rectangle.

(1) angle ABC = 90 degrees --> we know nothing about other angles. Not sufficient.
(2) AB=CD --> opposite sides AB and CD are equal, clearly insufficient.

(1)+(2) Look at the diagram:
Attachment:
rectangle.PNG
It's possible quadrilateral to be a rectangle (case ABCD1) and it's also possible quadrilateral not to be a rectangle (case ABCD2). Not sufficient.

saxenashobhit wrote:
E

for rectangle = all have to be 90 and opp sides equal
1. ABC= 90 : dont know about other angles - insuff
2. AB= CD , other sides may or may not be equal - insuff

together - not necessarily a rectangle, may be a square - insuff
Ans is E

metallicafan wrote:
E

It may be a square.

It's not necessary ABCD to be square (look at the diagram, it can be simple rectangle). In fact if we knew that ABCD is a square then statements would be sufficient, because square is a special type of rectangle, which means that every square is a rectangle (but not vise-versa).

Hope it helps.

HI Bunnel,

One doubt. Here it is mentioned that angle ABC are 90 degrees. and quadrilateral have total of 360 degree. so fourth one should be 90 degree.

then why you have mentioned following statement.

angle ABC = 90 degrees --> we know nothing about other angles. Not sufficient

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 52182

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18 Apr 2014, 03:32
PathFinder007 wrote:
Bunuel wrote:
agnok wrote:

1. angle ABC = 90 degrees
2. AB=CD

A rectangle is a quadrilateral with four right angles - this is necessary and sufficient condition for quadrilateral to be a rectangle.

(1) angle ABC = 90 degrees --> we know nothing about other angles. Not sufficient.
(2) AB=CD --> opposite sides AB and CD are equal, clearly insufficient.

(1)+(2) Look at the diagram:
Attachment:
rectangle.PNG
It's possible quadrilateral to be a rectangle (case ABCD1) and it's also possible quadrilateral not to be a rectangle (case ABCD2). Not sufficient.

saxenashobhit wrote:
E

for rectangle = all have to be 90 and opp sides equal
1. ABC= 90 : dont know about other angles - insuff
2. AB= CD , other sides may or may not be equal - insuff

together - not necessarily a rectangle, may be a square - insuff
Ans is E

metallicafan wrote:
E

It may be a square.

It's not necessary ABCD to be square (look at the diagram, it can be simple rectangle). In fact if we knew that ABCD is a square then statements would be sufficient, because square is a special type of rectangle, which means that every square is a rectangle (but not vise-versa).

Hope it helps.

HI Bunnel,

One doubt. Here it is mentioned that angle ABC are 90 degrees. and quadrilateral have total of 360 degree. so fourth one should be 90 degree.

then why you have mentioned following statement.

angle ABC = 90 degrees --> we know nothing about other angles. Not sufficient

Thanks

Yes, the Sum of Interior Angles of a polygon is $$180(n-2)$$ degrees, where $$n$$ is the number of sides (so is the number of angles). Thus the sum of the interior angles of a quadrilateral is 180*2=360 degrees.

But knowing that one of the angles of a quadrilateral is 90 degrees does not mean that the other angles must also be 90 degrees. The sum of the remaining three angles must be 360-90=270 degrees. So, the remaining three angles can be 100, 100 and 70 or 100, 110, and 60, ...

Hope it's clear.

Hope it's clear.
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10 May 2014, 11:00
Q1.
statement1>parallelogram
statement2>rectangle only if statement1 is true
Q2.
Q3
statement1>rectangle meaning all angles are 90
statement2> rhombus...
Math Expert
Joined: 02 Sep 2009
Posts: 52182

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11 May 2014, 05:04
ravishankar1788 wrote:
Q1.
statement1>parallelogram
statement2>rectangle only if statement1 is true
Q2.
Q3
statement1>rectangle meaning all angles are 90
statement2> rhombus...

Please note that the OA is E, not C. Check here: is-quadrilateral-abcd-a-rectangle-100729.html#p778263

Hope it helps.
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12 Jan 2018, 20:09
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Re: Is quadrilateral ABCD a rectangle? &nbs [#permalink] 12 Jan 2018, 20:09
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