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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."

Source: http://tylertarver.com

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