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03 Apr 2012, 07:27
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C
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Difficulty:
15%
(low)
Question Stats:
68% (00:39) correct
32%
(00:35)
wrong
based on 455
sessions
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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.
(1) Three angles of a quadrilateral are 90 degrees each.
(2) 3 sides of a quadrilateral are equal in length.
03 Apr 2012, 07:31
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[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?
(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?
03 Apr 2012, 08:23
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#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.
#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.
