Medians in a triangle proof

1. Jan 16, 2005

Perplexing

I know that the 3 medians of a triangle split the triangle into 6 similair triangles with equal area.

I wish to know the proof for this using simple geometry.

2. Jan 16, 2005

dextercioby

How do you know that??Did someone tell u,or you just invented it??

Daniel.

PS.If someone did tell u,why didn't u ask for the proof??Did u buy it,just like that??In mathematics,things don't work that way...

3. Jan 16, 2005

vincentchan

let's say...
you have a triangle ABC...
D is the point in between A and B
E is the point in between B and C
F is the point in between C and A
and O is the point 3 median lines intersect each other....

area ADO=area BDO, area AFO=CFO, area BEO = CEO
area ABE=ACE

area ABO=ABE-BEO
area ACO=ACE-CEO
this implies ABO=ACO
use the same method, you can show AFP=FCO=ABO=ADO=BEO=CEO

4. Jan 16, 2005

dextercioby

So i think everything comes down to proving that the median of a side of a triangle divides the area enclosed by the triangle into 2 equisuperficial portions...

Can u show that??

BTW,the triangle does not have an area...

Daniel.

5. Jan 16, 2005

vincentchan

the base and the height of those two triangles have equal value

6. Jan 16, 2005

dextercioby

Well,Vincentchan,i was obviously asking the OP... :grumpy:

Daniel.

PS.I knew you could answer it... :tongue2: