Is Quadrilateral ABCD a square? 1) Diagonals of ABCD cut at 90 degree

Question

Is Quadrilateral ABCD a square?

1) Diagonals of ABCD cut at 90 degrees
2) One of the angles at vertices is 90 degrees

Source :   https://www.GMATinsight.com

0akshay0 · Accepted Answer

Hence option E is correct Hit Kudos if you liked it 8-)

chetan2u · Answer

Hi,

Firstly please change the Q tag from combinations to GEOMETRY...

Combined, 
It can be a square or a rhombus or some other Quadrilateral..

Insufficient

GMATinsight · Answer

Bunuel Request you to change the tagging from Combinations to Geometry... Apologies for the mistake while tagging initially but I guess I can't change it now

Bunuel · Answer

No worries. Changed the tags.

shravan2025 · Answer

Hello expert .

Is A not sufficient to ascertain that this is not square . at least in a square diagonals always doesn't bisect at 90 degree .

chetan2u · Answer

No, ..
Firstly diagonals of square always bisect at 90°
Secondly even if say we had a situation like you have mentioned, ans can be yes or no, so insuff

RaguramanS · Answer

1) Diagonals of ABCD cut at 90 degrees  Square or Rhombus 
2) One of the angles at vertices is 90 degrees  Square or Rectangle or Rhombus

1+2 >  Square or Rhombus

lostnumber · Answer

I'm confused

I had thought that Statement 1) established that the shape was either a square or rhombus. Then statement two tells us that one angle is 90 degrees. Since we know that in a Rhombus the opposite angles must be equal, we would know that there are two 90 degree angles. Since there are only two angles which must be equal and 180 degrees left, we would know the remaining angles are also 90. Then I see your diagram which clearly fits both 1+2, but also clearly is not a Rhombus (sides are not equal) so what am I missing? Can a quadrilateral have 90 degree diagonal bisectors without being a rhombus?

amanvermagmat · Answer

Hello

Actually, from first statement, its not necessary that the quadrilateral is a square or a rhombus only; the quadrilateral could also be a 'Kite' (where there are two pairs of adjacent sides equal to each other. Eg, A kite ABCD can have AB=BC and AD=CD but AB not equal to AD and in this case angles BAD and BCD will be equal to each other. And diagonals of a kite are also perpendicular to each other).

So even after combining the two statements, it could be a 'kite' as I explained above and it could have angle B = 90 degrees, yet still not a square. I have tried to make a small diagram to help you understand, though in the previous posts diagram was already neatly drawn by someone.

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Is Quadrilateral ABCD a square? 1) Diagonals of ABCD cut at 90 degree

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Is Quadrilateral ABCD a square? 1) Diagonals of ABCD cut at 90 degree

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