Is quadrilateral a square?

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Is quadrilateral a square? [#permalink]

03 Apr 2012, 07:27

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Is quadrilateral a square?

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

Bunnel : Kindly provide ur insight.

Thanks.

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Re: Is quadrilateral a square? [#permalink]

03 Apr 2012, 07:31

[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]

03 Apr 2012, 08:23

#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]

05 Apr 2012, 02:55

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] 05 Apr 2012, 02:55

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Is quadrilateral a square?

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