Is the quadrilateral a square?

Question

ABCD.png Is quadrilateral ABCD a square? (1) AB = BC = CD = DA (2) AC = BD In this question - How come the answer is C? In Square the diagonals bisect each other at 90 degrees and are equal. How do we know that diagonals are bisecting each other at 90 degrees?

Bunuel · Accepted Answer

ABCD.png Is quadrilateral ABCD a square? (1) AB = BC = CD = DA --> both square and rhombus have all four sides equal in length. Not sufficient. (2) AC = BD --> both square and rectangle have diagonals equal in length. Not sufficient. (1)+(2) ABCD is a square. Sufficient. Answer: C. Useful property: if the diagonals of a rhombus are equal, then that rhombus must be a square. So you can apply this for (1)+(2) and conclude that ABCD must be a square. Check Polygons chapter of Math Book for more useful properties and tips: math-polygons-87336.html Hope it helps.

madn800 · Answer

from 1 it is clear that it is either a rhombus or a square as all sides are equal.

from 2 it is established that it is a square as IN A RHOMBUS DIAGONALS ARE NOT EQUAL.

hence C.

Asifpirlo · Answer

square has equal sides and equal diagonals.
rhombus has equal sides but not equal diagonals.
so both together are sufficient...... Answer (C)

About the 2nd question, let p the point of intersection ofthe two diagonal AC and BD.
now angle PAB = angle PBA  
so angle APB has to be 90 or it will not be possible for the total angle surrounding the point P to be 360.
so diagonals have to bisect at 90 degress

chetan2u · Answer

Hi,
1) statement tells us all sides are equal. it could be a rhombus , a square etc.... insuff
2) stat 2 tells us that the diagonals are equal.. it could be a rectangle , a square or any other quad.. insuff

combined we know it can only be a square... suff

divyarathi15 · Answer

Hi!

We could also say from statement 1 that it could be any irregular quadrilateral (apart from being either a rhombus/sq). Again from statement 2 it can be concluded that the figure could be any irregular quad too. combining both cant it be concluded that the figure could be an irregular quadrilateral too?

Bunuel · Answer

harikrish · Answer

Solution:

Statement 1: It can be either a square or rhombus. Insufficient.
Statement 2: It can be either a square or a parallelogram or a rectangle.

Combining St 1 and St 2, It has to be a square.

Therefore the answer is Option C.

longhaul123 · Answer

I did this question in the following method. Correct me if i am wrong . From the statement 1 the quadrilateral can be a Rhombus or a square. Hence not sufficient. Now from statement 2 the quadrilateral is a rhombus or a square or a rectangle.
1 and 2 together C

Bunuel · Answer

A rhombus with equal diagonal is a square.

GMATBusters · Answer

Statement 2: It can be either a square or a rectangle or any equidiagonal quadrilateral Quadrilaterals with equal diagonal are called equidiagonal quadrilateral. Equidiagonal Quandrilateral.jpg

bumpbot · Answer

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Is the quadrilateral a square?

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Is the quadrilateral a square?

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