First we need to Prove that
is true for the triangle.
It is instructive to look at the three triangles that make up the large triangle ABC.
We can say that the areas of these three triangles add up to make the area of ABC.
If we divide everything on both sides by the area of ABC, then ABC/ABC will be 1.
Now, the area of a triangle is found by taking one half the product of the base and height.
We can tell from our sketch the following:
Using these to substitute, we obtain
This can be simplified to
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