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AD is median of ∆ABC and …

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AD is median of ∆ABC and E is the mid point of AD IF BE is produced to meet AC at F, then AF = one third of AC

Posted by Kiran Yadav 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Given AD is the median of ΔABC and E is the midpoint of AD.
Through D, draw DG || BF.
In ΔADG, E is the midpoint of AD and EF || DG.
By converse of midpoint theorem, we have
F is midpoint of AG and AF = FG ................. (1)
Similarly, in ΔBCF
D is the midpoint of BC and DG || BF
G is midpoint of CF and FG = GC .................(2)
From equations (1) and (2), we get
AF = FG = GC ...............................................(3)
From the figure we have, AF + FG + GC = AC
AF + AF + AF = AC [from (3)]
3 AF = AC
Hence, AF= {tex}\frac { 1 } { 3 }{/tex}AC.

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CBSE > Class 10 > Mathematics