In the given figure, points P, Q, R and S are respectively the mid points of side AB, side CD, diagonal BD and diagonal AC of quadrilateral ABCD. The quadrilateral PRQS is a
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In the given figure, points P, Q, R and S are respectively the mid points of side AB, side CD, diagonal BD and diagonal AC of quadrilateral ABCD. The quadrilateral PRQS is a
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Answer:
Given that ABCD is a parallelogram and P,Q,R,S are mid point of side AB,CD and diagonals BD,AC
In triangle ABC,
P and S are midpoints of side AB and AC
Therefore,
PS =1/2 BC and PS || BC ( mid point theorem). (1)
Similarly in traingle DBC,
Q and R are midpoints of side DB and DC
Therefore,
QR = 1/2 BC and QR || BC (mid point theorem). (2)
From (1) and (2)
PS = QR (since both PS and QR is equal to 1/2 BC ) and PS || QR ( since PS || QR || BC)
Similarly we can prove that ,
SQ = PR ( since SQ= PR = 1/2 AD) and SQ || PR || BC
Therefore PQRS is a parallelogram ( opposite sides are equal and parallel )