What is the converse to the triangle proportionality theorem?

Question

accessdenied · Answer

Do you know what the Triangle Proportionality Theorem says?

anonymous · Answer

it would surely help to know what the theorem said. converse of "if P then Q" is "if Q then P"

anonymous · Answer

If a line is parallel to one side of a triangle and also intersects the other two sides , the line divides the sides proportionally.

accessdenied · Answer

Yep, so the converse is pretty easy: we switch the first statement after "If..." and the last statement after the "then..." (usually there's a 'then' after the comma).
 As mentioned, if we had "If P, then Q" then the converse would be "If Q, then P"

anonymous · Answer

oh ok that helps a lot thanks

accessdenied · Answer

You're welcome.  :)

anonymous · Answer

If the line divides the sides proprtionally, then the line is parralel to one side of a triangle and also intersects the other two sides.  Would that be it then?

accessdenied · Answer

Yeah, that'd be correct.

anonymous · Answer

:) thx

accessdenied · Answer

* you may want to mention that its "two sides of a triangle" rather than "the sides" in the first part after "If.." since it might be clearer what we're referring to from the start.  :)

directrix · Answer

Following from above:
If a line intersects two sides of a triangle and divides them proportionally, then the line is parallel to the third side of the triangle.