He wants to prove that ABCD is a square with sides AB BC CD DA all equal.
Info. 1 tells us that the diagonals intersect and they have 90 degrees together, which doesn't really help.
2 tells us that the addition of the 2 opposite sides are equal. if we assume that AB+CD=BC+AD= 6 AB & CD, BC & AD could have different combinations like (4,2) (3,3) (2,4) (5,1) ..etc so we can't prove that they're all equal.
Thus there isn't sufficient info to prove that this is a square.
Geometry
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shovan85
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1. AC is perpendicular to BDKoala wrote:If ABCD is quadrilateral, is AB=BC=CD=DA?
1) AC is perpendicular to BD
2) AB+CD=BC+AD
OA is E
Think about the geometrical shapes (as quadrilateral) that has perpendicularly intersecting diagonals.
Being a quadrilateral a square, or a Rhombus, or a Kite can have perpendicular. Though square and rhombus has all the sides equal, Kite does not have equal sides.
Thus insufficient.
2. AB+CD=BC+AD
Take simple numbers to verify.
3+4 = 2+5 (=7) so does this mean that 3 = 4 = 2 = 5? Never.
Thus insufficient.
IMO E
PS: If you have any kind of concerns about geometrical figure have a look at the below image for an idea. (Honestly I did not know what is a Kite (in terms of geometrical shape
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Rahul@gurome
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Statement 1: AC is perpendicular to BD.Koala wrote:If ABCD is quadrilateral, is AB=BC=CD=DA?
1) AC is perpendicular to BD
2) AB+CD=BC+AD
As there is no restrictions on the lengths of the sides, they can be same or different.
Not sufficient
Statement 2: AB + CD = BC + AD
There can be various possible combinations of lengths satisfying this condition.
Not sufficient
1 & 2 Together: Choose AB = AD and CD = AD, then statement 2 satisfies and we can make AC perpendicular to BD (as shown in the figure below) but still lengths of all the sides are not same.
Same case for AB = BC and CD = AD.
Not sufficient.
The correct answer is E.
No. The question is asking for whether ABCD is a rhombus or not.N:Dure wrote:He wants to prove that ABCD is a square with sides AB BC CD DA all equal.
Square is a special type of rhombus where all the angles are right angle.
Rahul Lakhani
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Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
