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16 Sep 2014, 01:23
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If \(ABCD\) is a quadrilateral, is \(AB = BC = CD = DA\)?
(1) AC is perpendicular to BD
(2) \(AB + CD = BC + AD\)
(1) AC is perpendicular to BD
(2) \(AB + CD = BC + AD\)
06 Dec 2014, 06:13
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Official Solution:
If \(ABCD\) is a quadrilateral, is \(AB = BC = CD = DA\)?
(1) AC is perpendicular to BD.
This statement implies that the diagonals are perpendicular to each other. In this case, \(ABCD\) could be a kite (answer NO), a rhombus (answer YES), or a square, which is a special type of rhombus (answer YES). Not sufficient.
(2) \(AB+CD=BC+DA\).
This statement implies that the sum of opposite sides is equal. Not sufficient.
(1)+(2) Combining the two statements, \(ABCD\) could be a kite (see the diagram below) - answer NO, or a square/rhombus - answer YES. Not sufficient.
Answer: E
If \(ABCD\) is a quadrilateral, is \(AB = BC = CD = DA\)?
(1) AC is perpendicular to BD.
This statement implies that the diagonals are perpendicular to each other. In this case, \(ABCD\) could be a kite (answer NO), a rhombus (answer YES), or a square, which is a special type of rhombus (answer YES). Not sufficient.
(2) \(AB+CD=BC+DA\).
This statement implies that the sum of opposite sides is equal. Not sufficient.
(1)+(2) Combining the two statements, \(ABCD\) could be a kite (see the diagram below) - answer NO, or a square/rhombus - answer YES. Not sufficient.
Answer: E
General Discussion
20 Sep 2015, 11:19
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I think bunuel explanation is more than sufficient. Thanks. The diagrams helped. I had trouble imagining the object, but then again I suck at geometry.
