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Quadrilaterals
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14/07/2021 12:09 pm
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Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.
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14/07/2021 12:10 pm
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.