Prove that the line passing through the triangle such that it is parallel to one side of the triangle divides the triangle's other two sides proportionally.

Questions:
1. What is the only constraint on the line passing through the triangle?
2. What do you notice about the "parts" of the other two sides of the triangle?
3. Is the ratio under "Proportional segments" the scale ratio? why or why not?
3. When the line passes through such that it is parallel to the third side what can be said about the two triangles formed? (smaller orange and larger blue)
4. If the triangles are similar, turn on the box to compare the segment to the overall side length. What does this ratio represent? How can we use it to find the length of BC?