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

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Bunuel
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Is quadrilateral ABCD a square? (1) ABCD is a rectangle whose diagona [#permalink] Is quadrilateral ABCD a square? (1) ABCD is a rectangle whose diagona   26 May 2021, 04:30
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55% (hard)

Question Stats:

47% (01:10) correct 53% (01:09) wrong based on 113 sessions
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Is quadrilateral ABCD a square?

(1) ABCD is a rectangle whose diagonals intersect at right angles.
(2) AC, a diagonal of ABCD, is also the hypotenuse of isosceles right triangles ABC and ADC.
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CrackverbalGMAT
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Is quadrilateral ABCD a square? (1) ABCD is a rectangle whose diagona [#permalink] Is quadrilateral ABCD a square? (1) ABCD is a rectangle whose diagona   26 May 2021, 05:13
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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
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Bunuel
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Re: Is quadrilateral ABCD a square? (1) ABCD is a rectangle whose diagona [#permalink] Is quadrilateral ABCD a square? (1) ABCD is a rectangle whose diagona   29 May 2021, 06:45
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Bunuel
Is quadrilateral ABCD a square?

(1) ABCD is a rectangle whose diagonals intersect at right angles.
(2) AC, a diagonal of ABCD, is also the hypotenuse of isosceles right triangles ABC and ADC.

Check Properties of Polygons Questions for similar problems.

23. Geometry




24. Coordinate Geometry




25. Triangles




26. Polygons




27. Circles




28. Rectangular Solids and Cylinders




29. Graphs and Illustrations



For other subjects:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.
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Re: Is quadrilateral ABCD a square? (1) ABCD is a rectangle whose diagona [#permalink] Is quadrilateral ABCD a square? (1) ABCD is a rectangle whose diagona   09 Jun 2021, 10:01
CrackVerbalGMAT
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.

PLEASE EXPLAIN THIS
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CrackverbalGMAT
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Is quadrilateral ABCD a square? (1) ABCD is a rectangle whose diagona [#permalink] Is quadrilateral ABCD a square? (1) ABCD is a rectangle whose diagona   21 Aug 2021, 18:39
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Vibhatsu
CrackVerbalGMAT
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.

PLEASE EXPLAIN THIS

Can a rhombus be a rectangle? Or is a rhombus obtained from a parallelogram when all sides turn equal?
What figure is a rectangle whose diagonals intersect at right angles?
Please refer to the links shared above by Bunuel to clarify on properties of the quadrilaterals.
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Is quadrilateral ABCD a square? (1) ABCD is a rectangle whose diagona [#permalink]
21 Aug 2021, 18:39
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