NandishSS wrote:

chetan2u wrote:

Bunuel wrote:

Is quadrilateral ABCD a square?

(1) A = C = 90º

(2) AB = AD

Ans will not be C but E..

statement I..

A=C=90

the triangle can be rectangle or square or any other possiblity too..

Insuff

statement II

AB=AD

nothing much

insuff

combined..

you can still have it as any other quadrilateral or as a square

see attached figureE

chetan2u Bhai,

How could be A = C = 90º in the first fig?

Hi Nandish

I think it IS indeed possible for a quadrilateral ABCD to have AB=AD, angle A = angle C = 90 degrees, and yet not be a square.

I have attached a pic of a figure similar to that of Chetan's first figure. If you would look at my pic, I first made AB=AD = 3 cm each, with an angle of 90 degrees between them. Then I made a tilted long line DX from D (this line is obviously NOT inclined at 90 with AD) - then on this line DX I chose one particular point C, from where CB will be aligned at 90 degrees to DX.

In my figure, DC is < 3 and CB is > 3. So its a figure slightly similar to Chetan's figure, where both conditions of question are being satisfied, yet its not a square.

Attachments

IMG_20180214_203201_3.jpg [ 23.12 KiB | Viewed 1158 times ]