Discover the metric relationship that exists between some special segments intercepted on two transversals by a family of lines, explore the proof of this property step by step, and then test yourself with the questions that follow.
Does the converse of this theorem hold?[br]State it, then explain or prove your answer, possibly using examples or counterexamples.
In a triangle [math]ABC[/math], with base [math]AB[/math], the segment [math]MN[/math] joins the midpoint of the side [math]AC[/math] with the midpoint of side [math]BC[/math].[br]What can you say about segment [math]MN[/math]?[br]Is it true that [math]BC=2MN[/math]? [br]Explain your answer, possibly using examples or counterexamples.