ABC is a triangle in which D is the midpoint of BC and E is the midpoi – InterviewSolution

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1.	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)`.
Answer» 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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