if ABCD is a quadrilateral, is AB = BC=CD=DA?
Statement I . AC is perpendicular to BD
Statement II . AB+CD= BC+ AD
The above conditions can be proved for kite as well which is also a quadrilateral by the way, and so not necessary that all the sides are congruent...
Kite has opposite sides congruent just like a parallelogram...
Hence the answer is E.
Hope this really helped...
By the way what is the source of this question... This seems to be a 700 level question...
Yaar GMAT out syllabus questions bhi poochhte hain yaar...
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if ABCD is a quadrilateral, is AB = BC=CD=DA?
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Mike@Magoosh
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At the risk of being nit-picking, I will point out that a kite has two pairs of adjacent congruent sides, unlike a parallelogram, which has two pairs of opposite congruent sides.
When a quadrilateral has both opposite sides congruent and adjacent sides congruent, that means it must be equilateral --- a rhombus, which is both a parallelogram and a kite.
Sorry to belabor a minor distinction, but I didn't want any of the readers to be confused.
With respect,
Mike
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