G.3.11.2 Parallel Segments

When a segment splits two sides of a triangle proportionally (let's nickname that side the "side splitter"), we already know many things:
  • 2 similar triangles are created
  • corresponding angles are congruent
  • the side splitter is parallel to other side
  • the side splitter is proportional to other side
Today we will be looking a new relationship:
  • the side splitter splits the two sides proportionally
                . Below is the triangle we looked at last week. We noticed that the scale factor that would take ADE to ACB is 4, and many people also noticed that sides EC and DB are 3 times as long as AE and AD. So, today we can see: