Q9 of 28 Page 112

The mid-points of the sides BC, CA and AB of a triangle ABC are respectively D, E and F. Then prove that EF bisects AD.


Construction: Join DE and DF.


In ΔABC, D and E are the mid points of BC and AC.


∴ DE || AB


DE = 1/2 AB


Now DE||AB


⇒ FA||DE ….. (1)


Similarly EA||DF ….. (2)


From (1) and (2),


EAFD is parallelogram.


As diagonals of ||gm bisects each other,


EF will bisect AD.

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