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Hello Mate!
Given : ABCD is a quadrilateral where E, F, G and H are mid points.
To prove : EFGH is ||gm.
To construct : Join BD.
Proof : Since E and H are mid points
EH = ½ BD and EH || BD __(i)
Since G and F are mid points,
GF = ½ BD and GF || BD __(ii)
From equation (i) and (ii) we get,
EH = GF and EH || GF.
Hence a quadrilateral whose one pair of sides are equal and parallel then quadrilateral is parallelogram.
Q.E.D
Have great future ahead!
Given : ABCD is a quadrilateral where E, F, G and H are mid points.
To prove : EFGH is ||gm.
To construct : Join BD.
Proof : Since E and H are mid points
EH = ½ BD and EH || BD __(i)
Since G and F are mid points,
GF = ½ BD and GF || BD __(ii)
From equation (i) and (ii) we get,
EH = GF and EH || GF.
Hence a quadrilateral whose one pair of sides are equal and parallel then quadrilateral is parallelogram.
Q.E.D
Have great future ahead!
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