lostnumber wrote:

0akshay0 wrote:

GMATinsight wrote:

Is Quadrilateral ABCD a square?

1) Diagonals of ABCD cut at 90 degrees

2) One of the angles at vertices is 90 degrees

Source: http://www.GMATinsight.comHence option E is correct

Hit Kudos if you liked it

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?

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.

Attachments

IMG_20180417_111909.jpg [ 15.83 KiB | Viewed 533 times ]