page_title: Intercept theorem
section_title: Height of the Cheops pyramid
hierarchical_section_title: Intercept theorem / Applications / Measuring and survey / Height of the Cheops pyramid
context_page_description: The intercept theorem, also known as Thales' theorem or basic proportionality theorem, is about ratios of various line segments that are created if two intersecting lines are intercepted by a pair of parallels. It is equivalent to the theorem about ratios in similar triangles. Traditionally it is attributed to Greek mathematician Thales.
context_section_description: According to some historical sources the Greek mathematician Thales applied the intercept theorem to determine the height of the Cheops' pyramid. The following description illustrates the use of the intercept theorem to compute the height of the pyramid. It does not however recount Thales' original work, which was lost.
  Thales measured the length of the pyramid's base and the height of his pole. 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. This yielded the following data:
  height of the pole (A): 1.63 m
  shadow of the pole (B): 2 m
  length of the pyramid base: 230 m
  shadow of the pyramid: 65 m
  From this he computed
  Knowing A,B and C he was now able to apply the intercept theorem to compute
caption: measuring pieces