Please give me the best way for solving the problem of class 9th ncert math of Quadrilaterals chapter of math of class 9th of exercise 8.2 of question no 6 what is the tricky way for solving this question Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.
AnilSinghBoraGuru
Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other. Q.6
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Let ABCD be a quadrilateral and P, Q, R and S are the mid points of 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, they will bisect each other.