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ABCD is a quadrilateral in which P, Q,...

ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA. AC is a diagonal. Show that : (i) `S R` `||` `A C` and `S R=1/2A C` (ii) `P Q = S R` (iii) PQRS is a parallelogram

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In the triangle, `Delta ACD`, `S` and `R` are midpoints of `AD` and `CD`.
So, from Midpoint theorem, we can say that, `SR||AC` and `SR = 1/2AC`->(1)
Similarly, in the triangle, `Delta ACB`, `P` and `Q` are midpoints of `AB` and `CB`.
So, from Midpoint theorem, we can say that,
`PQ||AC` and `PQ= 1/2AC`->(2)
From (1) and (2),
...
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