Question

Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other​

Answer 1

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Answer 2

Given:-

• ABCD is a quadrilateral P,Q,R & S are the midpoints of the respective sides.

To Prove:-

• PR and QS bisect each other

Proof:-

By midpoint Theorem:-

•  Join PQ,QR,RS,PS

• Join diagonals AC and BD

• In ΔABC,

→P and Q r the midpoints of AB and BC respectively

→Therefore by midpoint theorem, PQ is parallel to AC and PQ=1/2AC

→In the same way prove that SR is parallel to AC and SR=1/2AC

→Therefore, since the opposite sides are equal and parallel PQRS is a parallelogram

→In a parallelogram diagonals bisect each other

[Hence Proved!!]