# In a triangle ABC, E is the mid point of median AD.Show that ar (BED)=1/4 ar(ABC)

2
by srosyghque

2015-10-28T12:40:50+05:30

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We know that,
The median of a triangle divides the triangle into two triangles of equal area.

AD is the median of ΔABC
Therefore,

BE is the median of ΔABD
Therefore,
But
ar(ΔADB) =1/2 ar(ΔABC)    (from equation (1))

Therefore,

ar(ΔBED) =1/2[1/2 ar(ΔABC)]

ar(ΔBED) =1/4 ar(ΔABC)
2015-10-28T14:13:50+05:30

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Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Area of triangle ADB = 1/2 * altitude * DB = 1/2 * altitude  * DC
= 1/2 * altitude * (BC/2 )  = 1/2 * area of triangle ABC

similarly,
area of triangle  BED = 1/2 * base DE * altitude from B
= 1/2 * base EA * altitude from B
= 1/2 * (AD/2) * altitude from B
= 1/2 * area of triangle ADB

area of triangle DEB = 1/4 * area of triangle ABC