Question

ABCD is a quadrilateral in which P,Q,R and S are mid -points of the AB,BC,CD,and DA . 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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Answer 1

Answer:

R.E.F.Image.

In △ABC, P is the mid - point

of AB and Q is the mid point

of. BC.

By mid point theorem, we have

PQ∥AC and PQ=21AC ___ (1)

111ly in In ADC, R is mid pt. of CD and S is of AD

By mid point theorem

SR∥AC and SR=21Ac ___(2)

From (1) and (2) we get

PQ∥SR and PQ = SR

we know that in a quadrilateral opposite 

sides are equal and parallel then it is a 

parallelogram.

∴PQRS is a parallelogram.