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In the adjoining figure. AD and BE are t...

In the adjoining figure. AD and BE are two medians of `DeltaABC.` `IfDF"||"BE,"then prove that"CF=1/4AC.`

Text Solution

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E is the mid-point of line AC.
`thereforeCE=1/2AC" "...(1)`
In `DeltaABE,`
Since, D is the mid-point of CB and `DF"||"BE`
`therefore"F will be the mid-point of CE."" "("coverse of mid-point theorem")`
`implies" "CF=1/2CE`
`implies" "CF=1/2xx1/2AC" "["from"(1)]`
`implies" "CF=1/4AC`
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