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ABC is a triangle in which D is the midp...

`ABC` is a triangle in which `D` is the midpoint of `BC` and `E` is the midpoint of `AD`.
Prove that `ar(triangleBED)=(1)/(4)ar(triangleABC)`.

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Given : `A` `triangle`ABC in which `D` is the midpoint of `BC` and `E` is the important of `AD`.
To PROVE : `ar(triangleBED)=(1)/(4)ar(triangleABC)`.
Proof : `D` is the midpoint of BC `rArr` `AD` is a median of `triangle` ABC
`rArr ar(triangleABD=ar(triangleACD)`
`[therefore " a median divides a " triangle " into two "triangle " of equal area"]`.
`rArr ar(triangleABD)=(1)/(2)ar(triangleABC)." "...(i)`
`E` is the midpoint of `AD` `rArr` `BE` is a median of `triangle` `ABD`
`rArr ar(triangleBED)=ar(triangleBEA)`
`[therefore " a median divides a " triangle " into two "triangle " of equal area"]`.
`rArr ar(triangleBED)=(1)/(2)ar(triangleABD)=(1)/(2){(1)/(2)ar(triangleABC)}" " ["using (i)"]`
`rArr ar(triangleBED)=(1)/(4)ar(triangleABC)`.
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