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Question
In a parallelogram PQRS, M and N are the midpoints of the opposite sides PQ and RS respectively. Prove that
MN bisects QS.
Solution
M and N are the mid-points of PQ and RS respectively.
⇒ MN || QR
Let MN intersect QS at point O.
We know that the segment drawn through the mid-point of one side of a triangle and parallel to the other sides bisects the third side.
In ΔSRQ, N is the mid-point of RS and ON || QR
∴ O is the mid-point of SQ
⇒ OQ = OS ....(iii)
⇒ ON bisects QS
⇒ MN bisects QS.
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