Show that, the line segments joining the mid-points of opposite sides of a quadrilateral bisects each other.
Question:
Show that, the line segments joining the mid-points of opposite sides of a quadrilateral bisects each other.
Solution:
Let ABCD is a quadrilateral in which P, Q, R and S are mid-points of sides AB, BC, CD and DA respectively.
So, by using mid-point theorem we can say that
SP ∥ BD and SP = (1/2) BD .... (i)
Similarly in ΔBCD
QR ∥ BD and QR = (1/2) BD .... (ii)
From equations (i) and (ii), we have
SP ∥ QR and SP = QR
As in quadrilateral SPQR, one pair of opposite sides is equal and parallel to each other.
So, SPQR is a parallelogram since the diagonals of a parallelogram bisect each other.
Hence PR and QS bisect each other.
