Question

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

Answer 1

Answer:

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Answer 2

: Solution

➝ 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.