Question

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

Answer 1

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 )