Q. 194.1( 11 Votes )

Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.

Answer :

ABCD is a quadrilateral


P,Q,R,S are mid points of sides AB,BC,CD and DA


In ∆ABC , P and PQ are the mid points of AB and AC respectively


So, by using mid point theorem,



PQ││AC and PO ……………….(i)


Similarly in ∆BCD


RS││AC and RS =


From rquation (i) and (ii)


PQ││RS and PQ=RS


Similarly, we have


PSQR and PS=QR


Hence , PQRS is a parallelogram.


Since, diagonals of a paralleleogram bisects each other


Hence, PR and QS bisect each other proved


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