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20 Nov 2018, 10:58
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B
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:
58% (01:21) correct
42%
(01:08)
wrong
based on 81
sessions
History
Date
Time
Result
Not Attempted Yet
Is quadrilateral XYZW a rhombus?
(1) Diagonals of quadrilateral XYZW intersect at 90 degrees.
(2) X, Y, Z, W are the mid-points of sides AB, BC, CD and DA respectively of a rectangle ABCD.
(1) Diagonals of quadrilateral XYZW intersect at 90 degrees.
(2) X, Y, Z, W are the mid-points of sides AB, BC, CD and DA respectively of a rectangle ABCD.
20 Nov 2018, 22:58
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Is quadrilateral XYZW a rhombus?
(1) Diagonals of quadrilateral XYZW intersect at 90 degrees.
If the sides are equal, yes... As in this case the diagonals will bisect each other
If sides are not equal or the diagonals do not bisect each other... No
Insufficient
(2) X, Y, Z, W are the mid-points of sides AB, BC, CD and DA respectively of a rectangle ABCD.
Since all are joining the midpoints of sides, all sides of XYZW will be equal.
Also the diagonals will be parallel to the sides and so will bisect each other at 90.
Sufficient as answer is yes
B
(1) Diagonals of quadrilateral XYZW intersect at 90 degrees.
If the sides are equal, yes... As in this case the diagonals will bisect each other
If sides are not equal or the diagonals do not bisect each other... No
Insufficient
(2) X, Y, Z, W are the mid-points of sides AB, BC, CD and DA respectively of a rectangle ABCD.
Since all are joining the midpoints of sides, all sides of XYZW will be equal.
Also the diagonals will be parallel to the sides and so will bisect each other at 90.
Sufficient as answer is yes
B
15 Apr 2020, 06:20
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amanvermagmat
Solution
Step 1: Analyse Question Stem
- • XYZW is a quadrilateral
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: Diagonals of quadrilateral XYZW intersect at 90 degrees
- • We don't know whether all the sides of XYZW are equal or not
• We know that the diagonals of kite, square and rhombus intersect each other at 90 degree
- o XYZW can be a kite, rhombus, or square
Statement 2: X, Y, Z, and W are the midpoints of the sides AB, BC, CD, and DA, respectively of the rectangle ABCD.
Let 2l and 2b be the length and breadth of the rectangle ABCD.
- • \(XY = YZ = ZW=ZW = \sqrt{l^2+b^2}\)
- o All the sides of the XYZW are equal.
- o XZ is parallel to BC and AD
o YW is parallel to AB and CD
XZ and YW bisect each other perpendicularly.
