Usually in school, you learn how to construct a parallelogram with compass and straightedge. But today, I am gonna show you how to construct a parallelogram with only one ruler. Of course, you need a piece of paper, a pencil, a hand, and your brain as well, etc …

Actually the method is very simple, even an eight year old can do it I promise. So here it is:

- Draw a quadrilateral (4-sided shape), any quadrilateral will do even the non-convex one.
- Find the midpoint of all four sides with your ruler.
- Connect those four midpoints together and you are done.

Here are some examples.

The proof is very simple.

Let the four points , , , be the vertices of a quadrilateral.

Then the four midpoints are

Find the slopes of the sides and show that the opposite sides are parallel:

Therefore *PQRS* is a parallelogram.

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