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14/07/2021 11:45 am
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ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see Figure). AC is a diagonal. Show that:
(i) SR || AC and SR = 1/2 AC
(ii) PQ = SR
(iii) PQRS is a parallelogram.
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14/07/2021 11:48 am
(i) In ΔDAC
R is the mid point of DC and S is the mid point of DA.
Thus by mid point theorem, SR || AC and SR = 1/2 AC
(ii) In ΔBAC
P is the mid point of AB and Q is the mid point of BC.
Thus by mid point theorem, PQ || AC and PQ = 1/2 AC
SR = 1/2 AC
PQ = SR
(iii) SR || AC ........ from question (i)
PQ || AC ......... from question (ii)
⇒ SR || PQ – from (i) and (ii)
also, PQ = SR
PQRS is a parallelogram.