Question

Show that the line segment joining the midpoints of opposite sides of a quadrilateral bisect each other.

Answer 1

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In 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 other.

Answer 2

Step-by-step explanation:

By this method we can also prove this sir