Question

The line segment joining the mid point of opposite sides bisect each other

Answer 1

ΔADC, S and R are the midpoints of AD and DC respectively. Recall that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and half of it. Hence SR || AC and SR = (1/2) AC  → (1) Similarly, in ΔABC, P and Q are midpoints of AB and BC respectively.⇒ PQ || AC and PQ = (1/2) AC  → (2)  [By midpoint theorem] From equations (1) and (2), we get PQ || SR and PQ = SR  → (3) Clearly, one pair of opposite sides of quadrilateral PQRS is equal and parallel. Hence PQRS is a parallelogram Hence the diagonals of parallelogram PQRS bisect each other. Thus PR and QS bisect each otherN