abc is a triangle in which d is the mid point of bc and e is the mid point of ad . prove that (bed)=1/4ar(abc)
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In triangle ABC,
D is the median
> ar( ADB) = ar(ADC) = 1/2 ar(ABC) ........1
In triangle ADB,
E is the median
> ar( ABE) = ar(DBE) = 1/2 ar(ADB) ...........2
From 1 and 2,
ar(BED ) = 1/2*1/2 ar(ABC)
> ar(BED) = 1/4 ar(ABC)
D is the median
> ar( ADB) = ar(ADC) = 1/2 ar(ABC) ........1
In triangle ADB,
E is the median
> ar( ABE) = ar(DBE) = 1/2 ar(ADB) ...........2
From 1 and 2,
ar(BED ) = 1/2*1/2 ar(ABC)
> ar(BED) = 1/4 ar(ABC)
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