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Is quadrilateral a square?

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Is quadrilateral a square? [#permalink]

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New post 03 Apr 2012, 06:27
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Is quadrilateral a square?

(1) Three angles of a quadrilateral are 90 degrees each.
(2) 3 sides of a quadrilateral are equal in length.
[Reveal] Spoiler: OA
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Re: Is quadrilateral a square? [#permalink]

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New post 03 Apr 2012, 06:31
[quote="balas"]Is Quadrilateral a square?
(1) Three angles of a quadrilateral are 90 degrees each.
(2)3 sides of a quadrrilateral are equal in length.


OA: C


(1) Three angles of a quadrilateral are 90 degrees each: Then the quadrilateral can be a rectangle or a square.
(2) 3 sides of a quadrrilateral are equal in length: Then the quadrilateral can be a rhombus or a square.
(1) + (2): The quadrilateral has to be a square.

Hence C.
Is my reasoning correct?
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Re: Is quadrilateral a square? [#permalink]

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New post 03 Apr 2012, 07:23
#1: If all four sides are equal, it still may not be a square. For example, if all angles are not 90* then it is a Rhombus. Not sufficient.
#2: Three angles 90* means the fourth angle has to be 90* too. However, if a quadrilateral has all four angles equal to 90*, does it mean it is a square? No. It could be a rectangle. Not sufficient.


Combining #1 and #2: The quadrilateral must have all four angles 90*. Since 3 sides are equal, the fourth one must be equal to these three since the pair of opposite sides must be equal if all four angles are 90*. Hence, the quadrilateral must be a square.

Hope that was clear.
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Re: Is quadrilateral a square? [#permalink]

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New post 05 Apr 2012, 01:55
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balas wrote:
Is quadrilateral a square?

(1) Three angles of a quadrilateral are 90 degrees each.
(2)3 sides of a quadrrilateral are equal in length.



we need two things
1) sides are equal
2) all angles 90

from statement 1)
no info about sides

INSUFFICIENT

from statement 2)

no info about angles
INSUFFICIENT

FROM BOTH 1 AND 2

we have info both sides and angles

SUFFICIENT

Hence C.

Hope this helps...!!!
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Re: Is quadrilateral a square? [#permalink]

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New post 27 Jan 2018, 20:19
balas wrote:
Is quadrilateral a square?

(1) Three angles of a quadrilateral are 90 degrees each.
(2) 3 sides of a quadrilateral are equal in length.



according to statement 1, the quadrilateral can be a square or a rectangle
not sufficient

according to statement 2, the quadrilateral can be a square or a rhombus
not sufficient

taking statements (1 + 2) together we can say with certainty that the quadrilateral is a square

C the answer

thanks, and cheers with kudos
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Re: Is quadrilateral a square? [#permalink]

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New post 27 Jan 2018, 23:29
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balas wrote:
Is quadrilateral a square?

(1) Three angles of a quadrilateral are 90 degrees each.
(2) 3 sides of a quadrilateral are equal in length.


Check Properties of Polygons Questions from our Special Questions Directory.

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Hope it helps.
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Re: Is quadrilateral a square?   [#permalink] 27 Jan 2018, 23:29
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