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Quadrilateral

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by goyalsau » Sat Oct 02, 2010 2:07 pm
If ABCD is a quadrilateral, is AB=BC=CD=DA?

1.AC is perpendicular to BD

2.AB+CD=BC+DA
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Source: — Data Sufficiency |
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by shovan85 » Sat Oct 02, 2010 2:18 pm
IMO A
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by goyalsau » Sat Oct 02, 2010 2:24 pm
shovan85 wrote:IMO A
Correct answer is E
I don't know why?
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by shovan85 » Sat Oct 02, 2010 2:33 pm
goyalsau wrote:
shovan85 wrote:IMO A
Correct answer is E
I don't know why?
What is the source? I have a doubt on OA
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by goyalsau » Sat Oct 02, 2010 2:39 pm
One of my friend has given me the practice questions in CD.
So source is Friend.......

let it be I think some experts can make this point really clear
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by shovan85 » Sat Oct 02, 2010 2:42 pm
goyalsau wrote:One of my friend has given me the practice questions in CD.
So source is Friend.......

let it be I think some experts can make this point really clear
I can bet when a quadrilateral has it diagonal perpendicular then it has to be a Rhombus
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by reply2spg » Sat Oct 02, 2010 4:53 pm
Correct answer must be E

Actually question is asking whether quadrilateral is square?
goyalsau wrote:If ABCD is a quadrilateral, is AB=BC=CD=DA?

1.AC is perpendicular to BD - Diagonals of rectangle and square are always perpendicular.

2.AB+CD=BC+DA - This property is also same for square and rectangle
Sudhanshu
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by goyalsau » Sat Oct 02, 2010 9:03 pm
reply2spg wrote:Correct answer must be E

Actually question is asking whether quadrilateral is square?
goyalsau wrote:If ABCD is a quadrilateral, is AB=BC=CD=DA?

1.AC is perpendicular to BD - Diagonals of rectangle and square are always perpendicular.

2.AB+CD=BC+DA - This property is also same for square and rectangle
Thanks sudanshu,
I think i have to cramp all those rules,
Will search for all those quadrilateral rules before approaching same problem like this again.
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by shovan85 » Sat Oct 02, 2010 10:37 pm
reply2spg wrote:Correct answer must be E

Actually question is asking whether quadrilateral is square?
goyalsau wrote:If ABCD is a quadrilateral, is AB=BC=CD=DA?

1.AC is perpendicular to BD - Diagonals of rectangle and square are always perpendicular.

2.AB+CD=BC+DA - This property is also same for square and rectangle
can you please review: diagonals of rectangle are perpendicular to each other? I dont think so. Only Rhombus has the diagonal perpendicular. A square is a Rhombus. IMO A.

https://en.wikipedia.org/wiki/Rhombus#Properties
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by narik11 » Sun Oct 03, 2010 9:54 am
shovan85 wrote:
reply2spg wrote:Correct answer must be E

Actually question is asking whether quadrilateral is square?
goyalsau wrote:If ABCD is a quadrilateral, is AB=BC=CD=DA?

1.AC is perpendicular to BD - Diagonals of rectangle and square are always perpendicular.

2.AB+CD=BC+DA - This property is also same for square and rectangle
can you please review: diagonals of rectangle are perpendicular to each other? I dont think so. Only Rhombus has the diagonal perpendicular. A square is a Rhombus. IMO A.

https://en.wikipedia.org/wiki/Rhombus#Properties
From option 1 : Diagonals are perpendicular to each other . So it can either be a square or a rhombus
From option 2:Sum of Pair of opposite sides are equal . So all sides are equal. Therefore it can be a square or a rhombus.

So option E.

Also note u can differentiate between a square and a rhombus using the angles. In square all angles are 90,whereas in rhombus it may or may not be the case. That's why all squares are rhombus
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by shovan85 » Sun Oct 03, 2010 11:07 am
narik11 wrote:
shovan85 wrote:
reply2spg wrote:Correct answer must be E

Actually question is asking whether quadrilateral is square?
goyalsau wrote:If ABCD is a quadrilateral, is AB=BC=CD=DA?

1.AC is perpendicular to BD - Diagonals of rectangle and square are always perpendicular.

2.AB+CD=BC+DA - This property is also same for square and rectangle
can you please review: diagonals of rectangle are perpendicular to each other? I dont think so. Only Rhombus has the diagonal perpendicular. A square is a Rhombus. IMO A.

https://en.wikipedia.org/wiki/Rhombus#Properties
From option 1 : Diagonals are perpendicular to each other . So it can either be a square or a rhombus
From option 2:Sum of Pair of opposite sides are equal . So all sides are equal. Therefore it can be a square or a rhombus.

So option E.

Also note u can differentiate between a square and a rhombus using the angles. In square all angles are 90,whereas in rhombus it may or may not be the case. That's why all squares are rhombus
So u agree that from 1 we sure this quadrilateral is a rhombus.
what is rhombus? all sides are same right ;)
so is nt it AB=BC=CD=DA?
Thus A is sufficient. :)
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by goyalsau » Sun Oct 03, 2010 7:27 pm
So u agree that from 1 we sure this quadrilateral is a rhombus.
what is rhombus? all sides are same right ;)
so is nt it AB=BC=CD=DA?
Thus A is sufficient. :)


I completely agree that 1 is sufficient.

But can you please explain ,
Why we are not considering statement 2, There must be some reason behind it.

Because reply2msg is saying that
AB+CD=BC+DA - This property is also same for square and rectangle

and narik is saying that
From option 2:Sum of Pair of opposite sides are equal . So all sides are equal. Therefore it can be a square or a rhombus.

According to me it will definitely not be rectangle. Because in rectangle opposite sides are equal so its not possible.
But if it a square or a rhombus then it actually gives us the answer.
Or may be is it a trapezoid or kite.
Or may be any thing ....
Guys what do you think..
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by goyalsau » Sun Oct 03, 2010 7:57 pm
goyalsau wrote:If ABCD is a quadrilateral, is AB=BC=CD=DA?

1.AC is perpendicular to BD


2.AB+CD=BC+DA
Hey guys i just did search on Quadrilaterals and this is what i find.

Definition of KITE
Hey, it looks like a kite. It has two pairs of sides. Each pair is made up of adjacent sides that are equal in length. The angles are equal where the pairs meet. Diagonals (dashed lines) meet at a right angle, and one of the diagonal bisects (cuts equally in half) the other.

Definition of RHOMBUS
A rhombus is a four-sided shape where all sides have equal length.
Also opposite sides are parallel and opposite angles are equal.
Another interesting thing is that the diagonals (dashed lines in second figure) of a rhombus bisect each other at right angles.


With these Two definition ONE thing is Sure that option A is not sufficient.
Because it can be a Kite or a Rhombus


I am still not to figure out the second statement.....
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by shovan85 » Sun Oct 03, 2010 9:51 pm
Great man!! Very Insightful.

So, I can see E now :) Thanks.
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by goyalsau » Sun Oct 03, 2010 10:31 pm
shovan85 wrote:Great man!! Very Insightful.

So, I can see E now :) Thanks.
Can you please explain Why statement 2 is not considerable.
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