. Thales Theorem and Angle Bisector Theorem . . Introduction Thales, ( - BC (BCE)) the most famous Greek mathematician and philosopher lived around seventh century BC (BCE).
He possessed knowledge to the extent that he became the first of seven sages of Greece. Thales was the first man to announce that any idea that emerged should be tested scientifically and only then it can be accepted. In this aspect, he did great investigations in mathematics and astronomy and discovered many concepts. He was credited for providing first proof in mathematics, which today is called by the name “Basic Proportionality Theorem”.
It is also called “Thales Theorem” named after its discoverer. The discovery of the Thales theorem itself is a very interesting story. When Thales travelled to Egypt, he was challenged by Egyptians to determine the height of one of several magnificent pyramids that they had constructed. Thales accepted the challenge and used similarity of triangles to determine the same successfully, another triumphant application of Geometry.
Since X , X and H are known, we can determine the height H of the pyramid. m m R P Q Thales ( - BC (BCE)) X H H X Line of sight Fig. . H X H X N Q P M L O R o To understand the basic proportionality theorem or Thales theorem, let us do the following activity.
Activity Take any ruled paper and draw a triangle ABC with its base on one of the lines. Several parallel lines will cut the triangle ABC . Select any one line among them and name the points where it meets the sides AB and AC as P and Q . Can we find the ratio of AP PB and AQ QC .
By measuring AP , PB , AQ and QC through a scale, verify whether the ratios are equal or not? Try for different parallel lines, say MN and RS . Now find the