Review write-ups for Assignments 1 to 12.

__PT A__: Consider
any triangle ABC. Select a point P inside the triangle and draw
lines AP, BP, and CP extend to their intersections with the opposite
sides in points D, E, and F respectively.

Explore (AF) (BD) (EC) and (FB) (DC) (EA) for various triangles and locations of P.

__PT B:__ Consider
the following ratio.

This triangle shows that the above segments have a special relationship. They are equal, in fact.

Click here for a GSP sketch with measurements.

Click here for a GSP sketch of P outside the triangle.

While exploring the following triangle, the point P, although arbitrary, holds an important position. With this point similiar triangles can be constructed.

__PT C: __What is
the ratio of triangle ABC and triangle DEF when P is inside the
triangle ABC?

The ratio will be grater than or equal to four. The ratio will equal to four when D, E, and F are located at the midpoints of lines BC, CA, and AB.

Click here for a measurement of the areas of triangle ABC and DEF.

Course Evaluation