Question

Points D, E and F are the mid-points of sides of A ABC. Point G is
the centroid of A ABC. Show that, the point G is the centroid of
A DEF also.





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Answer 1

Answer:

In ΔADH and ΔABF: DE and BC are parallel to each other as midpoint theorem.

∠ADH = ∠ABF (corresponding angles)

∠AHD = ∠AFB ( " )

∠DAH = ∠BAF (Common)

Hence, ΔADH ~ ΔABF

AD/ AB = DH/BF AD/2AD = DH/BF (AD = DB) BF = 2DH

(i) Similarly in ΔAEH & ΔAFC CF = 2EH

(ii) From (i) & (ii) DH = EH Similarly you can calculate for all the three sides,

Thus, G is the centroid of ΔDEF

Step-by-step explanation:

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