In triangle ABC
D is the midpoint of aide BC
E is the mindpoint of seg AD
AE=ED
BD=DC
show A(triangle BER)=1/4 A(Triangle ABC)
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Given -- A AABC.
D is the mid-point of BC and E is the mid-point of AD.
To prove: ar (ABED)=1/4 ar (AABC)
Proof: Since AD is the median of AABC,
Therefore, ar (AABD) = ar (AADC)
=> ar (AABD) = 1/2 ar (AABC)
Since BE is the median of ABD,
Therefore, ar (ABED)= ar (ABAE)
=> ar (ABED) = 1/2 ar (AABD)
= 1/2 x 1/2 ar (AABC)
(using (1)
Hence, ar (BED)=1/4 ar (AABC)
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