Theorem 6.4 Triangle Proportionality Theorem
If a line is parallel to one side of a triangle and intersects the other sides, it divides the two sides proportionally.
Theorem 6.5 Converse of the Triangle Proportionality Theorem
If a line divides two sides of a triangle proportionally, then it is parallel to the third side.
Source: McDougal Littel High School Geometry
"How to prove and use properties of triangle midsegments. Yeah, it's that important."
If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally.
In the figure shown, if , then and
Example found at the bottom of this page: http://hotmath.com/hotmath_help/topics/parallel-lines-and-transversals.html