Investigate the phenomenon resulting from the following steps in Sketchpad:[1] Construct...

Investigate the phenomenon resulting from the following steps in Sketchpad:

[1] Construct ∆ABC.

[2] Locate D any point on side .

[3] Construct a line through D parallel to , then select its intersection E with . (What geometric principle predicts that this line must intersect ?)

[4] Display the ratios CD/CA and DE/AB side by side.

As you drag D on , what happens to these ratios? Try proving your observation is correct based on geometric principles so far (note that we have not yet come to similar triangles).