abcd is a point in which pqrs are mid point of the sides ab,bc, cd,and da respecively show that pqrs is a parallelogram
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GIVEN: A,B,C,D are any points .P,Q,R,S are mid points of sides AB , BC ,CD and DA respectively.
CONSTRUCTION :In quad ABCD the diagonals AC and BD are joined.
PROOF:
In triangle ABD ,
S &P are mid points of sides AB and AD respectively .
Therefore by mid-point theorem,
PS||BD &
PS=1/2 BD --Eq.1
In triangle CBD,
By mid point theorem
RQ||BD
RQ=1/2BD --Eq.2
we get PS||BD and BD||RQ
therefore PS||RQ
In Eq 1 and 2 we get:
PS=1/2BD
RQ=1/2BD
PS =RQ
As in quad PQRS opposite sides are parallel and equal therefore PQRS is a parallelogram
Hope this helps:)
CONSTRUCTION :In quad ABCD the diagonals AC and BD are joined.
PROOF:
In triangle ABD ,
S &P are mid points of sides AB and AD respectively .
Therefore by mid-point theorem,
PS||BD &
PS=1/2 BD --Eq.1
In triangle CBD,
By mid point theorem
RQ||BD
RQ=1/2BD --Eq.2
we get PS||BD and BD||RQ
therefore PS||RQ
In Eq 1 and 2 we get:
PS=1/2BD
RQ=1/2BD
PS =RQ
As in quad PQRS opposite sides are parallel and equal therefore PQRS is a parallelogram
Hope this helps:)
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