Kate Berryman
cavaleri@uga.edu
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Altitudes and Orthocenters
Given triangle ABC. Construct the Orthocenter H. Let points D, E, and F be the feet of the perpendiculars from A, B, and C respectfully.
Prove:
We can start with the formula for the area of a triangle.
In our case: So we can have: We also know that:
If we look at our smaller triangles, we see that: So another way to calculate area is:
We recall: Then we divid by AD*BC:
Since: We can substitute our denominators: Therefore, we arrive at:
Now let's prove: We proved above that the follow is true: Now let's look at our triangle.
We can easily see that: Or So by a little substitution we get the following:
