Click the hide/show checkbox to explore the angle bisector & side proportionality OR the parallel line "Side Splitter" proportionality in a triangle. Drag points to change the triangle or slide the parallel line intersection.
Would either of these properties be true in other convex polygons? If so, under what conditions is it true or when is it not true? How can you prove these properties (in the triangle case)? Show that the proportions (in the "side splitter" case) are equivalent to the scale factor.