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Show that a median of a triangle divi...

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

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GIVEN A `triangle` ABC in which AD is median.
TO PROVE `ar(triangleABD)=ar(triangle ADC)`.
CONSTRUCTION Draw AL`bot`BC.
PROOF Since D is the midpoint of BC, we have
BD = DC.
Now, BD = DC
`rArr (1)/(2)BDxxAL=(1)/(2)DCxxALrArr ar(triangleABD)=ar(triangleADC)`.
Hence,a median of a triangle divides it into two triangle of equal area.
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