The progenitor of Greek mathematics
Thales is also said to have determined the distance of ships from the coastline by measuring from the end points of a standing line on the shore the angles between the standing line and the rays of sight to a ship and finding out the distance by a scaled construction - domyhomework.club . He used the congruence theorem wsw, which he also formulated as a theorem, and actually also the main similarity theorem.
He also used the similarity of triangles in another case. When he was in Egypt, the priests wanted to put him to the test and asked him to determine the height of a pyramid - https://domyhomework.club/math-homework/ . Thales then measured the length of the shadow of the pyramid, the length of a staff stretched vertically from it into the ground and the shadow it cast. Using a ratio equation, he thus calculated the height quite accurately, to the astonishment of the priests.
Thales left no records, but reports by his contemporaries and his descendants bear witness to his work and his achievements, so that he may rightly be called the progenitor of Greek mathematics.
Theorem of Thales:
Every circumferential angle above a semicircle (or above the diameter of a circle) is a right angle.
If you draw the diameter of a circle and several triangles ABC whose third vertex lies inside, outside or exactly on the circle's line, you will find that the angle BCA becomes smaller - statistics homework helper - and smaller from the inside to the outside. First it is obtuse, then it is acute. In one case a right angle occurs.