in triangle ABC if D,E,F are midpoints of sides BC,AC,AB respectively then prove that the centroid of triangle - Maths -

Question

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

Rahul Raj · Accepted Answer

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

regards

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 ...