Two angles are considered complementary when the sum of their amplitudes is equal to 90º. In Euclidean geometry, the two acute angles that form a right triangle are complementary. The reason for this is that the internal sum of the angles of any triangle is 180 °, so if one of them is right, ie 90 °, the other two are complementary (they also measure 90 °).
In the following drawing, we can see that `AhatBD + DhatBC` is always equal to 90º.
Created with GeoGebra by Vitor Nunes
Move the point `D` to obtain different angles amplitudes. Check that the sum is always 90º
Euclidean geometry, like all other mathematics, was born of the human need to understand what is around us. This geometry had its origin with the great mathematician Euclid, born about 330 BC in Syria. At the request of King Ptolemy I, he was invited to teach mathematics at the Alexandria Academy. With the passage of time gained prominence by the way he taught Geometry and Algebra. Although these disciplines were already known to mathematicians before Euclid, he was noted for having done a more in-depth study of the contents, and organized them logically, creating one of the greatest masterpieces of mathematics: "The Elements." This work consists of thirteen books that include arithmetic, geometry and algebra.