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# Is quadrilateral ABCD a square? (1) ABCD is a rectangle whose diagona

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Re: Is quadrilateral ABCD a square? (1) ABCD is a rectangle whose diagona [#permalink]
CrackVerbalGMAT wrote:
Solution:

St(1):- ABCD is a rectangle whose diagonals intersect at right angles.

Sufficient information to provide that ABCD is a square.

St (2):-AC, a diagonal of ABCD, is also the hypotenuse of isosceles right triangles ABC and ADC.

=>Adjacent sides equal; angle ABC and angle ADC are 90 degrees with the diagonal bisecting the other two angles creating

angle angle BAC=angle BCA =Angle ACD =angle DAC=45 degree each

=>ABCD is a square. (Sufficient) (option d)

Devmitra Sen
GMAT SME

This is Wrong. Why not B?

As, ABCD is a rectangle whose diagonals intersect at right angles: This can be a square or a rhombus .

So,B is sufficient.

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Is quadrilateral ABCD a square? (1) ABCD is a rectangle whose diagona [#permalink]
Top Contributor
Vibhatsu wrote:
CrackVerbalGMAT wrote:
Solution:

St(1):- ABCD is a rectangle whose diagonals intersect at right angles.

Sufficient information to provide that ABCD is a square.

St (2):-AC, a diagonal of ABCD, is also the hypotenuse of isosceles right triangles ABC and ADC.

=>Adjacent sides equal; angle ABC and angle ADC are 90 degrees with the diagonal bisecting the other two angles creating

angle angle BAC=angle BCA =Angle ACD =angle DAC=45 degree each

=>ABCD is a square. (Sufficient) (option d)

Devmitra Sen
GMAT SME

This is Wrong. Why not B?

As, ABCD is a rectangle whose diagonals intersect at right angles: This can be a square or a rhombus .

So,B is sufficient.