in triangle ABC  if D,E,F are midpoints of sides BC,AC,AB respectively .then prove that the centroid of triangle DEF  and triangle  ABC is same ...

dear student

using midpoint theorem, the line joining the midpoint of two sides of a triangle is parallel to the third side


so in the given figure

EF is parallel to BC, DE to AB and DF to AC

so AEDF is parallelogram
diagonals bisect each other
so FH=HE
DH is the median of triangle DEF
similarly, EI and FJ are medians
these meet at G, which is also the centroid of triangle ABC


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