Question

What is difference between:
1) Basic Proportionality theorem: If a line parallel to one side of a triangle intersects the other two sides in two different points, then it divides these sides into segments that are proportional.
2) Corollary: If a line parallel to one side of a triangle intersects the other two sides in different points, then it cuts off segments that are proportional to the sides of the triangle.
Please, help. My prof said that they are slightly different to each other but I don't see it.

Answer 1

main theorem is called "side splitter theorem"

corollary simply comes from "similar triangles"

Answer 2

the main theorem says \(\dfrac{AD}{AE} = \dfrac{DB}{EC}\)


corollary says \(\dfrac{AD}{AE} = \dfrac{AB}{AC}\)

Answer 3

Wow!!!
Thank you so much. I got you. :)