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Is quadrilateral ABCD a square?

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Is quadrilateral ABCD a square? [#permalink]

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New post 28 Sep 2015, 03:05
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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.
[Reveal] Spoiler: OA

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Re: Is quadrilateral ABCD a square? [#permalink]

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New post 28 Sep 2015, 04:41
Answer should be A

I also had the same issue. I went through all the properties of different quadrilaterals.

1. ABCD is a rectangle and if diagnals intersect at 90 degree, square is the only option. Suff.

2. In the second case, it can be either square or a kite as per the given properties Insuff.
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Re: Is quadrilateral ABCD a square? [#permalink]

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New post 28 Sep 2015, 04:52
Answer is D, the second cannot be a kite
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Re: Is quadrilateral ABCD a square? [#permalink]

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reto wrote:
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.

I am always struggling with such questions. Any sources to prepare for those?


reto, look at the attached picture of quadrilateral family in GMAT. It is taken from https://en.wikipedia.org/wiki/Rhombus

Statement 2, is sufficient to answer as it can only be a square. Kite would have been possible had the statement mentioned that the triangles are isosceles but not necessarily right angled.

Statement 1 eliminates rhombus as it is not a rectangle.

Thus D is the correct answer.
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Symmetries_of_square.svg.png
Symmetries_of_square.svg.png [ 30.7 KiB | Viewed 1566 times ]


Last edited by ENGRTOMBA2018 on 28 Sep 2015, 10:32, edited 1 time in total.
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Re: Is quadrilateral ABCD a square? [#permalink]

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New post 28 Sep 2015, 05:07
apoorva2890 wrote:
Answer should be A

I also had the same issue. I went through all the properties of different quadrilaterals.

1. ABCD is a rectangle and if diagnals intersect at 90 degree, square is the only option. Suff.

2. In the second case, it can be either square or a kite as per the given properties Insuff.


It can not be a kite as the resulting triangle must be RIGHT ANGLED ISOSCELES triangle. Kite does not provide that. Thus, square is the only option.
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Re: Is quadrilateral ABCD a square? [#permalink]

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New post 28 Sep 2015, 09:59
Engr2012 wrote:
reto wrote:
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.

I am always struggling with such questions. Any sources to prepare for those?


reto, look at the attached picture of quadrilateral family in GMAT.

Statement 2, is sufficient to answer as it can only be a square. Kite would have been possible had the statement mentioned that the triangles are isosceles but not necessarily right angled.

Statement 1 eliminates rhombus as it is not a rectangle.

Thus D is the correct answer.


Thanks - I also found this overview here: quadrilateral-properties-136155.html#p1106572
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Re: Is quadrilateral ABCD a square? [#permalink]

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New post 28 Sep 2015, 10:07
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reto wrote:
Engr2012 wrote:
reto wrote:
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.

I am always struggling with such questions. Any sources to prepare for those?


reto, look at the attached picture of quadrilateral family in GMAT.

Statement 2, is sufficient to answer as it can only be a square. Kite would have been possible had the statement mentioned that the triangles are isosceles but not necessarily right angled.

Statement 1 eliminates rhombus as it is not a rectangle.

Thus D is the correct answer.


Thanks - I also found this overview here: quadrilateral-properties-136155.html#p1106572


Instead of just rote memorizing these properties make sure to draw them out so that you remember how to apply these properties as well.
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Re: Is quadrilateral ABCD a square? [#permalink]

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New post 08 Jan 2018, 11:01
I don't understand why (1) is Suff.

Don't the diagonals of rhombus intersect at 90º?
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Re: Is quadrilateral ABCD a square? [#permalink]

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New post 08 Jan 2018, 19:50
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Fernandocma wrote:
I don't understand why (1) is Suff.

Don't the diagonals of rhombus intersect at 90º?


(1) says that ABCD is a rectangle. Rectangular rhombus is a square.

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




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Re: Is quadrilateral ABCD a square?   [#permalink] 08 Jan 2018, 19:50
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