Final Assignment:

**Ratios **

** **

By Amber Krug

** **

** **Given any triangle ABC and point P, we have:

My conjecture is that __AF__
* __CE__ * __BD__
= 1.

FB EA DC

We can see this by constructing
similar triangles and substituting the resulting similar ratios in to see that
the product is in fact 1.

The ratio of the areas of
triangles ABC and DEF will always be greater than or equal to 4. Click
here to see when the ratio is greater than 4. The ratio is equal to 4 when triangle DEF is the medial
triangle of ABC.