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.
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