Constructing regular polygons given one side

Link to the exercise (Mongge)

Line, ray and line segment

Thales´Theorem (measuring the Pyramid)

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points the other two sides are divided in the same ratio.

According to some historical sources the Greek mathematician Thales applied the intercept theorem to determine the height of the Cheops' pyramid. 

Thales measured the length of the pyramid's base and the height of his pole (a long stick). Then at the same time of the day he measured the length of the pyramid's shadow and the length of the pole's shadow.