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Is quadrilateral ABCD a Rectangle?

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Is quadrilateral ABCD a Rectangle?  [#permalink]

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New post 31 Jul 2017, 06:43
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A
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E

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Is quadrilateral ABCD a Rectangle?

Statement 1: AB is perpendicular to BC and is parallel to CD.
Statement 2: AC=BD
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Re: Is quadrilateral ABCD a Rectangle?  [#permalink]

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New post 31 Jul 2017, 07:14
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DH99 wrote:
Is quadrilateral ABCD a Rectangle?

Statement 1: AB is perpendicular to BC and is parallel to CD.
Statement 2: AC=BD



Hi...
I tells us AB and CD are perpendicular to BC. But we don't know about AD..
CD could be stretching towards for infinity length.
Insufficient
II tells us nothing much...

Combined..
The diagonals are EQUAL and AB and CD are perpendicular to BC..
So ABCD is a rectangle..
Sufficient

C
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Re: Is quadrilateral ABCD a Rectangle?  [#permalink]

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New post 31 Jul 2017, 07:21
Hi@chetan2u.I solved using this method.Is the method correct?

From1: Trapezium,Rectangle
From 2: Isoscles Trapezium,Sq,Rectangle
1+2>> Rectangle
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Re: Is quadrilateral ABCD a Rectangle?  [#permalink]

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New post 31 Jul 2017, 07:32
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DH99 wrote:
Hi@chetan2u.I solved using this method.Is the method correct?

From1: Trapezium,Rectangle
From 2: Isoscles Trapezium,Sq,Rectangle
1+2>> Rectangle


HI..

you are correct.
ONLY observation I have --
statement II leads toany quadrilateral, since we do not know where do they cut each other..
so it could be square, trapezium, any quadrilateral..
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Re: Is quadrilateral ABCD a Rectangle?  [#permalink]

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New post 31 Jul 2017, 08:29
If we combine two statements why it can't be square..Let me know where I am going wrong.
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Re: Is quadrilateral ABCD a Rectangle?  [#permalink]

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New post 31 Jul 2017, 08:34
vivek2k70 wrote:
If we combine two statements why it can't be square..Let me know where I am going wrong.


Hi vivek2k70, combining we can get a square as well as a rectangle(Either).Since, square is a type of rectangle.So combining the two is sufficient.
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Re: Is quadrilateral ABCD a Rectangle?  [#permalink]

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New post 31 Jul 2017, 08:42
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vivek2k70 wrote:
If we combine two statements why it can't be square..Let me know where I am going wrong.


A square is a type of rectangle.
So, if a quadrilateral is a square, then it it also a rectangle.
In fact, a square also a type of parallelogram AND a type of rhombus

MORE HERE:

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

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New post 04 Mar 2019, 04:07
DHAR wrote:
Is quadrilateral ABCD a Rectangle?

Statement 1: AB is perpendicular to BC and is parallel to CD.
Statement 2: AC=BD



#1
we dont know about AD and BC sides ; are they also perpendicular or not
not sufficient
#2
ac=bd ; no info of what they can determine

from 1&2
ABCD is quadrilateral with diagonal AC & DB and sides which are perpendicular
IMO C sufficient to conclude ABCD is a rectangle
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Re: Is quadrilateral ABCD a Rectangle?  [#permalink]

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New post 28 Nov 2019, 05:56
Hey,

How can option c be correct.
we are getting at 2 conclusion it is either rectangle or square.
No where length and angle between diagonals mentioned.

SO how you can say it is C.
in up comments some one is telling square is kind of rectangle ???/how ??

Please experts..explain why answer is not E ??
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Re: Is quadrilateral ABCD a Rectangle?  [#permalink]

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New post 28 Nov 2019, 07:35
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JiddiHuMain wrote:
Hey,

How can option c be correct.
we are getting at 2 conclusion it is either rectangle or square.
No where length and angle between diagonals mentioned.

SO how you can say it is C.
in up comments some one is telling square is kind of rectangle ???/how ??

Please experts..explain why answer is not E ??


When we combine the statements, we have a quadrilateral in which the opposite sides are parallel, and each angle in the quadrilateral is 90 degrees.
This meets all of the requirements to be a rectangle.
So, the answer to the target question is "YES, quadrilateral ABCD is a rectangle"
Could ABCD also be a square? That's possible. But the question doesn't ask "Is ABCD a square"

Does that help?

Cheers,
Brent
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Re: Is quadrilateral ABCD a Rectangle?  [#permalink]

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New post 28 Nov 2019, 07:45
So here is possibility of yes or no

so how you are sure it is a rectangle ...now where is mentioned angle between diagonals ??

if angle between diagonal is 90 and all sides are equal then it will be not rectangular else it is rectangular..

so here convincing information is not available..


so we can't say it is rectangle..

if i am wrong please correct me.
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Re: Is quadrilateral ABCD a Rectangle?   [#permalink] 28 Nov 2019, 07:45
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