Final Assignment

Melissa Bauers Summer 2002

Part 1:

Review write-ups for Assignments 1 to 12.

Part 2:

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.

(AF) (BD) (CE)

(BF) (CD) (AE)


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.

Part 3

Course Evaluation

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