The Total solution for NCERT class 6-12
Show that the line segments joining the mid-points of the opposite sidesof a quadrilateral bisect each other.
Let ABCD be a quadrilateral and P, Q, R and S are the mid pointsof AB, BC, CD and DA respectively.
Now,
In ΔACD,
R and S are the mid points of CD and DA respectively.
, SR || AC.
Similarly we can show that,
PQ || AC,
PS || BD and
QR || BD
, PQRS is parallelogram.
PR and QS are the diagonals of the parallelogram PQRS. So, theywill bisect each other.