## Problem #001 - a dancing triangle

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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.

### Problem statement

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?

If you need any clarification whatsoever, feel free to ask in the comment section below.

### Solution

You can read the solution here to compare with your own solution.