1. Drawing an irrational length line

2. To draw an irrational length line, we can use Pythagoras’ Theorem in the right triangle. And copy the length that we get from the triangle with a compass.
Example:
To draw the line which is length.
We use the right triangle as shown in this page. 2 1
The red edge of the triangle is the line that we want to draw, it is the length line.
To draw a length line, we copy the red line twice using a compass, and paste it into a straight line, continue the first copy with the second copy.

3. Now!
Draw a length line.
1st step: Copy the length line using a compass from the right
triangle with the length of edges: 1, , and 2, that have
been made before
2nd step: draw a right triangle, with the length of the right edges
are and , then you will get the hypotenuse of
this triangle is
Important Conclusion: If you have to draw an irrational length line, you can use more than one steps, and draw more than one right triangle to get the length that you need.