Cevians

I am currently reading a problem on Cevian. A Cevian is a line which emanates from a vertex and fall on the opposite side. The problem is about to prove that the longest Cevian is greater than the sum of the parts which fall on the opposite sides. To prove this the author first shows that measure ofany cevian lies between the length of the two sides. So any given Cevian will always be smaller than the longest side. Then he constructs two parallel lines and get a similar triangle to the original triangle and shows that sum of the cevian parts are less than the longest side of the original triangle