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