Question

In triangle ABC,E is the midpoint of median AD,show that ar[BED]=1/4 ar[ABC]

Answer 1

given; AD is the median & E is the mid-point of AD.
since,AD is the median of the Triangle's ABC.
therefore, Ar.(ABC) =Ar.(ADC) (median divides the tri.into 2equal parts)
or,Ar(ABD)=half of Ar(ABC)...1
now, E is the mid point of the median AD
i.e,AE=ED
In Tir.ABD;
BE is the median of the tri.ABD
so,Ar(ABE)=Ar(BED)
or,Ar(BED)=half Ar(ABD)..2
putting the value of Ar(ABD),we get,
Ar(BED)=half of Ar(ABD)
=Ar(BED)=1\2*1\2•Ar(ABC)
=Ar(BED)=1\4(ABC)
******* hence, proved.....

Answer 2

Answer:

Step-by-step explanation:

hey here is your proof in above pics

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