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CBSE Class 9 Answered

ABCD is a parallelogram in which P, Q, R and S are the mid points of the sides AB, BC, CD and DA respectively. AC is a diagonal, show that PQRS is a parallelogram.
Asked by Topperlearning User | 11 Aug, 2017, 11:55: AM
answered-by-expert Expert Answer
ABCD is a quadrilateral; P, Q, R and S are the mid points of the sides AB, BC, CD and DA respectively.
Join AC.
In ABC, P and Q are the mid points of sides AB and BC respectively.
PQ  AC and PQ = begin mathsize 12px style 1 half end styleAC (i)         (by mid point theorem)
In ADC, R and S are the mid points of sides CD and AD respectively.
RS  AC and RS = begin mathsize 12px style 1 half end styleAC               (ii)        (by mid point theorem)
From (i) and (ii)
PQ  RS and PQ = RS                                   
In the quadrilateral PQRS one pair of opposite sides is equal and parallel.
 PQRS is a parallelogram.
Answered by | 11 Aug, 2017, 01:55: PM

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