This post's format will be a bit different from the usual and the first of a series of posts of this type. In this post, I will state a problem and then present my solution.
Let \([ABC]\) be any triangle. We now define a transformation of the triangle which moves one vertex and leaves the other two unchanged. To apply a transformation, start by picking the vertex you want to move. Assume it was \(C\). Consider the line that goes through \(C\) which is parallel to \([AB]\), and pick any point \(C'\) in it. Your transformed triangle is \([ABC']\). You can repeat this process as many times as you want.
Can the original triangle be transformed into a triangle where all sides where doubled? How/why?
Give it some thought...
If you need any clarification whatsoever, feel free to ask in the comment section below.
You can read the solution here to compare with your own solution.