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In Figure, A D\ a n d\ B E are medians o...

In Figure, `A D\ a n d\ B E` are medians of ` A B C\ a n d\ B E||D F` . Prove that `C F=1/4A C`
Consider `/_\ABC` Since AD is Median
`=>BD=BC`⋯(1)
Since BE is Median`=>AE=EC`⋯(2)
Consider `/_\BEC \Since\ BE∣∣DF`
By Basic Proportionality theorm, `=>BD/DC=EF/FC`
From (1)`=>CF=EF`
`=>CF=1/2 AE`
From (2)`=>CF=1/4AC`

Text Solution

Verified by Experts

Consider `/_\ABC` Since AD is Median
`=>BD=BC`⋯(1)
Since BE is Median`=>AE=EC`⋯(2)
Consider `/_\BEC \Since\ BE∣∣DF`
By Basic Proportionality theorm, `=>BD/DC=EF/FC`
From (1)`=>CF=EF`
`=>CF=1/2 AE`
From (2)`=>CF=1/4AC`
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