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 figure

E

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.

amanvermagmat, chetan2u, Bunuel,

Thanks for Solution, Will take it a learning

Happy Prepping

Bunuel
Amazing. You made this qoestion so easy.

the diagonal should bisect each other for the quad to be a square apart from each angle being 90

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