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20 Nov 2018, 10:54
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Difficulty:
85%
(hard)
Question Stats:
32% (01:27) correct
68%
(01:50)
wrong
based on 73
sessions
History
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Is Quadrilateral ABCD a rectangle?
(1) A, B, C, D are the mid-points of sides PQ, QR, RS and SP respectively of a parallelogram PQRS.
(2) Opposite angles of quadrilateral ABCD are supplementary, i.e, sum of angles A and C is 180 degrees; similarly sum of angles B and D is also 180 degrees.
(1) A, B, C, D are the mid-points of sides PQ, QR, RS and SP respectively of a parallelogram PQRS.
(2) Opposite angles of quadrilateral ABCD are supplementary, i.e, sum of angles A and C is 180 degrees; similarly sum of angles B and D is also 180 degrees.
20 Nov 2018, 23:07
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Is Quadrilateral ABCD a rectangle?
(1) A, B, C, D are the mid-points of sides PQ, QR, RS and SP respectively of a parallelogram PQRS.
When you join the midpoints of any quadrilateral ( so parallelogram is also included in it), it is a parallelogram. Therefore it is possible it is a rectangle or otherwise too.
Insufficient
(2) Opposite angles of quadrilateral ABCD are supplementary, i.e, sum of angles A and C is 180 degrees; similarly sum of angles B and D is also 180 degrees.
Nothing much
Insufficient
Combined
We know it is a parallelogram, so opposite angles are equal.
From II, we get total as 180, so each angle is 180)2=90
Thus opposite sides parallel and equal and all angles 90 means it is a rectangle.
Sufficient
C
(1) A, B, C, D are the mid-points of sides PQ, QR, RS and SP respectively of a parallelogram PQRS.
When you join the midpoints of any quadrilateral ( so parallelogram is also included in it), it is a parallelogram. Therefore it is possible it is a rectangle or otherwise too.
Insufficient
(2) Opposite angles of quadrilateral ABCD are supplementary, i.e, sum of angles A and C is 180 degrees; similarly sum of angles B and D is also 180 degrees.
Nothing much
Insufficient
Combined
We know it is a parallelogram, so opposite angles are equal.
From II, we get total as 180, so each angle is 180)2=90
Thus opposite sides parallel and equal and all angles 90 means it is a rectangle.
Sufficient
C
Mo2men
Joined: 26 Mar 2013
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21 Nov 2018, 02:30
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