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

PS∥QR 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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