http://209.85.48.8/9963/162/upload/p2206487.gif

The area must be equal.

How do I do this?

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- July 10th 2010, 11:00 PMCthul[Trigonometric Ratios] Dividing a triangle with equal area
http://209.85.48.8/9963/162/upload/p2206487.gif

The area must be equal.

How do I do this? - July 10th 2010, 11:18 PMAlso sprach Zarathustra
Use median from point C to AB (why?)

- July 10th 2010, 11:20 PMCthul
Oops, I forgot to mention the triangle has to have equal area.

Will the area be the same if I just divide it like that? - July 10th 2010, 11:21 PMAlso sprach Zarathustra
- July 10th 2010, 11:43 PMCthul
Thanks. I didn't know finding the median will make the area still equivalent.

- July 10th 2010, 11:49 PMundefined
There's a proof here. (The proof is for a stronger result.) This is related to the centroid being centre of mass for a thin triangular slab with uniform density.

- July 11th 2010, 05:54 AMSoroban
Hello, Cthul!

"Also Sprach" is absolutely correct.

We have with median drawn to side

. . Hence: .

Draw altitude from vertex to side

Code:`A`

o

*:* *

* : * *

* : * *

* : * *

* :h * *

* : * *

* : * *

* : * *

* : * *

B o * * * * + * * * * o * * * * * * * * * o C

M

Triangles and have equal bases and the same altitude.

. . Hence, they have equal areas.

A median*always*divides a triangle into two equal areas.