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Difficulty:
35%
(medium)
Question Stats:
60% (01:04) correct
40%
(01:06)
wrong
based on 538
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Date
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Is quadrilateral ABCD a rhombus?
(1) AC is perpendicular to BD
(2) AB + CD = BC +AD
M11-05
(1) AC is perpendicular to BD
(2) AB + CD = BC +AD
M11-05
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20 Dec 2014, 08:26
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Is quadrilateral \(ABCD\) a rhombus?
(1) \(AC\) is perpendicular to \(BD\).
This property holds true for both rhombi and kites, so this information alone is not sufficient to determine whether \(ABCD\) is a rhombus.
(2) \(AB + CD = BC + AD\).
This property is also true for both rhombi and kites, so this information alone is not sufficient to determine whether \(ABCD\) is a rhombus.
(1)+(2) Combining the two statements does not provide any additional information. Quadrilateral \(ABCD\) could still be either a rhombus or a kite. Not sufficient.
Refer to the image below for visualization:
Answer: E
(1) \(AC\) is perpendicular to \(BD\).
This property holds true for both rhombi and kites, so this information alone is not sufficient to determine whether \(ABCD\) is a rhombus.
(2) \(AB + CD = BC + AD\).
This property is also true for both rhombi and kites, so this information alone is not sufficient to determine whether \(ABCD\) is a rhombus.
(1)+(2) Combining the two statements does not provide any additional information. Quadrilateral \(ABCD\) could still be either a rhombus or a kite. Not sufficient.
Refer to the image below for visualization:
Answer: E
Attachments
Kite and Rhombus.png [ 167.86 KiB | Viewed 18732 times ]
16 May 2017, 02:35
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(1) Line segments AC and BD are perpendicular bisectors of each other.
Perpendicular bisector means it would divide the line into half and thus the quadrilateral formed by joining A,B,C,D will have equal side and that is the property of rhombus
Perpendicular bisector means it would divide the line into half and thus the quadrilateral formed by joining A,B,C,D will have equal side and that is the property of rhombus
