Show that a median of a triangle divides it into two triangles of equal area.

Explanation

Solution
Lets assume `ABC` be a triangle and Let `AD` be one of its medians.
In `/_\ ABD` and `/_\ ADC` the vertex is common and bases are equal.
Constructing `AE_|_ BC`.
Now area `(/_\ABD)`
`=1/2` `xx` base `xx` altitude of `/_\ ADB`
`=1/2 xx BD xx AE=1/2 xx DC xx AE(:'BD=DC)`
but `DC` and `AE` are the base and altitude of `/_\ ACD`
`= 1/2` `xx` base `DC` `xx` altitude of `/_\ ACD`
`=area/_\ ACD`
`=>area(/_\ ABD)=area(/_\ ACD)`
Hence proved.