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25 Jun 2018, 11:06
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Difficulty:
75%
(hard)
Question Stats:
33% (01:11) correct
67%
(01:18)
wrong
based on 101
sessions
History
Date
Time
Result
Not Attempted Yet
Is quadrilateral PQRS a parallelogram?
(1) P, Q, R, S are the mid-points of sides AB, BC, CD and AD respectively of a trapezoid ABCD.
(2) Diagonals of quadrilateral PQRS bisect each other.
(1) P, Q, R, S are the mid-points of sides AB, BC, CD and AD respectively of a trapezoid ABCD.
(2) Diagonals of quadrilateral PQRS bisect each other.
28 Jun 2018, 07:12
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amanvermagmat
With 90% wrong, it shows lack of properties of a parallelogram....
(1) P, Q, R, S are the mid-points of sides AB, BC, CD and AD respectively of a trapezoid ABCD.
When midpoints are joined of the four sides of ANY quadrilateral, it forms a parallelogram
look at the sketch..
ABCD is a quadrilateral and PQRS forms another quadrilateral by joining the midpoints..
join diagonal DB....
in triangle ADB, PQ will be parallel and half of the diagonal DB as PQ is bisecting the other two sides..
similarly SR is also parallel and half of DB..
thus PQ||DB||SR and PQ=SR
similarly for the set of other opposite sides
hence the quadrilateral is parallelogram
sufficient
(2) Diagonals of quadrilateral PQRS bisect each other.
Again this is the property of a quadrilateral- if diagonals bisect each other, it is a parallelogram
ca be proven by similar triangles and congruency..
sufficient
D
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Mo2men
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28 Jun 2018, 08:17
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chetan2u
Hi chetan2u
In statement 2, Could the figure be square or rectangular? or are both subset/special case of parallelogram so they must be considered parallelogram?
Thanks
