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if ABCD is a quadrilateral, is AB = BC=CD=DA?

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by [email protected] » Sat Feb 18, 2012 7:33 am
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...

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by Mike@Magoosh » Sat Feb 18, 2012 1:15 pm
[email protected] wrote:
Kite has opposite sides congruent just like a parallelogram...
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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https://gmat.magoosh.com/
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by dim » Mon Nov 02, 2015 7:21 am
Thank you very much Mike for the explanation.
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