Question

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

Answer 1

Answer:

construction: join BE

proof: AD is the median ,median divides a triangle into two triangles of equal area

= area [ABD]= area [ACD] ...........equation 1

= ar[ABD] =1/2 ar[ ABC]

in triangle ABDBE is the median , median divides a triangle into twa triangles of equal area .

=ar[ BED] =ar[BEA]

ar[BED] =1/2 ar[ ABD]

ar[ BED] =1/2*1/2ar[ABC]

=ar[BED]=1/4ar[ABC]

             HOPE IT HELPS ...............................

Answer 2

Step-by-step explanation:

Given:ABC is a triangle

AD is a median

E is mid point of AD

To prove: ar(BED)=1/4 ar(ABC)

Proof: In triangle ABC,

AD is median

ar(ABD)=ar(ACD) --1

In triangle ABD,E is mid point of AD

ar(ABE)=ar(BED)--2

In triangle ACD, E is the mid point of AD

ar(ACE)=ar(CED)--3

From 1,2,3

ar(ABE)=ar(BED)=ar(ACE)=ar(CED)

ar(ABC)=4ar(BED)

Therefore,ar(BED)=1/4 ar(ABC)

Hence proved