# In Δ ABC,AD is the median through A & E is the mid point of AD.BE is produced to meet AC in F.Prove that AF=1/3AC.

2
by simi

hey i got the answer but i don't have enough time . so i can't dear srryy

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by simi

hey i got the answer but i don't have enough time . so i can't dear srryy

Log in to add a comment

to prove:AF=1/3AC.

Construction:From point D draw DG parallel to BF.

Proof: so by Convere of mid point theorum we get F as the mid point of AG

⇒AF=AG(1)

similarly we have G as the mid point of CF

⇒FG=GC(2)

from 1 and 2 we get

AF=FG=GC (3)

now AF + FG + GC =AC

From (3) we get

AF+AF+AF=AC

3(AF)=AC

AF=1/3AC

hence prove .

Hope this helps

The Brainliest Answer!

AD is the median of triangle ABC.

E is the mid point of AD.BE produced meet ad at F.

Construction:From point D draw DG parallel to BF.

By mid point theorem we got F as the mid point of AG

-> AF=AG --------1

G as the mid point of CF

-> FG=GC--------------2

by one and two

AF = FG= GC ---------- 3

by the 3 rd equation

AF+AF+AF=AC

3×AF =AC

so 1/3 ac = af