Suppose you have a ruler of the unknown length. There are only two marks on the ruler exactly 2 cm apart.
The goal is by using such a ruler, a pencil and a piece of paper to draw on the paper a segment exactly 1 cm long.
How many dots will you have to uncover to reach the goal?
This is one of the basic solutions – 7 points are needed. All lines are drawn with the help of the ruler.
Figure 1. Draw two straight lines intersecting in point A.
Figure 2. Measure on two A-rays the following segments: AB = BC = 2cm, and AD = DE = 2cm.
Figure 3. Join D with B and E with C. DB is parallel to EC.
Figure 4. Measure 2 cm on EC – from point C. FC = 2cm.
Figure 5. Join A with F and then with G. The GB is the middle line of the ACF triangle (based on the fact DB is parallel to FC and that the distance between A and DB equals to the distance between DB and EC). That means GB equals 1cm – half of the triangle’s parallel side.