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Related Rates Triangles 1

Related rates problems often involve triangles-- since many relationships in the world in which we live can be boiled down to thinking about triangles. In this sketch you will become more familiar with one type of situation.
1) Drag point D. Notice how the sketch works. (Getting your head wrapped around what is going on is always the first step!) 2) What changes and what stays unchanged as a result of moving point D? (Just refinining your understanding of the relationship here.) 3) Suppose that AB = 2 cm, AC = 4 cm and AD = 1 cm, what would be the length of DE? (Now we are starting to quantify the relationships.) 4) How could you predict the length of DE if AD was just any random length? (Developing a function for the length of DE as a function of the length of AD. We are assuming the lengths of AB and AC are known.)