Thread: [Trigonometric Ratios] Dividing a triangle with equal area

The area must be equal.
How do I do this?

Use median from point C to AB (why?)

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?

Originally Posted by Cthul

Oops, I forgot to mention the triangle has to have equal area.

I have considered that already...

Thanks. I didn't know finding the median will make the area still equivalent.

Originally Posted by Cthul

Thanks. I didn't know finding the median will make the area still equivalent.

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.

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.