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Question

Assertion : In ΔABC, median AD is produced to X such that AD = DX. Then, ABXC is a parallelogram.
Reason : Diagonals AX and BC bisect each other at right angles.
Which of the following is correct?


A
If both assertion and reason are true and reason is the correct explanation of assertion
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B
If both assertion and reason are true but reason is not the correct explanation of assertion
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C
If assertion is true but reason is false
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D
If assertion is false but reason is true
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Solution

The correct option is C If assertion is true but reason is false
In quadrilateral ABXC, we have,
AD = DX [Given]
BD = DC [AD is given as median]
ADB = XDC [Vertically Opposite Angles]
Thus, ΔADB is congruent to ΔXCD by SAS congruency.


Hence, AB = XC [CPCT] (1)
BAD = CXD [CPCT]
BAD and CXD form a pair of alternate interior angles and since they are equal, AB||XC (2)
From (1) and (2), ABXC is proved to be a parallelogram, as we have proved that one pair of opposite sides are parallel and equal.
So, diagonals AX and BC bisect each other.

ABXC is a parallelogram
Assertion is true but reason is false.

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