The following Sketchpad project will illustrate one of the theorems of this section.[1] C...

The following Sketchpad project will illustrate one of the theorems of this section.

[1] Construct three parallel lines at random distances apart. (Draw the first line , locate arbitrary points C and D, then use Parallel Line under CONSTRUCT to obtain lines through C and D parallel to line .)

[2] Construct a point E on one line and point F on another, then construct line . Select the point G of intersection of with the third line.

[3] Display the ratio EF/FG on the screen.

As you drag E to change the slope of line , observe what happens to the ratio EF/FG. What theorem explains this behavior?