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16 Sep 2014, 00:43
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
61% (01:09) correct
39%
(01:16)
wrong
based on 225
sessions
History
Date
Time
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Not Attempted Yet
Is quadrilateral \(ABCD\) a rhombus?
(1) \(AC\) is perpendicular to \(BD\).
(2) \(AB + CD = BC + AD\).
(1) \(AC\) is perpendicular to \(BD\).
(2) \(AB + CD = BC + AD\).
16 Sep 2014, 00:43
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Official Solution:
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
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
General Discussion
