Is it possible to draw this picture without lifting the pen?

Some days ago, our math teacher said that he would give a good grade to the first one that will manage to draw this:

To draw this without lifting the pen and without tracing the same line more than once. It's a bit like the "nine dots" puzzle but here I didn't find any working solution. So I have two questions:

• is it really impossible?
• how can it be proven that it is impossible (if it's impossible)

[EDIT]: After posting this question, and seeing how it was easy for people to solve it, I noticed that I posted the wrong drawing. The actual one is eaxctly like that but with triangles on all sides, not only top and bottom. As it would make the current answers invalid, I didn't replace the picture.

Solution 1:

It is possible, and it's actually quite easy. Start on the red dot and move your pen according to numbers in a picture below.

Solution 2:

Here is one way, out of many.

As you can see, I started at one vertex and ended at the same vertex. Since the graph is connected, and every vertex has an even number of segments joined to it, you can start at any vertex and end there, covering all the segments.