Parallel Lines Proportionality Theorem

Move the points around to create new triangles.  Record the lengths listed in the table.  (You will have to add two smaller marked segments to find the length of the longer one.) Repeat twice to get values for all three Trials.

After filling in the table above with the segment lengths, calculate the ratios identified below. (Click the ratio button in the applet for the ratios in the first and third columns.)

Using the information found above, list the pairs of ratios that would make a proportion (i.e. they are equal). 

For those you ratios listed above, how are the segments in each ratio related to each other?  

Drag two points together (A and B, or F and D) to make a triangle. Generalize what you discovered about the ratios to find a shortcut to solving for the length (or a portion of the length) of the side of a triangle.