Theorems

Theorems in Geometry, like in other disciplines, are theoretical statements requiring proof using known true axioms. These statements are used to study various phenomena based on solving theoretical problems. The term «theorem» in translation from ancient Greek means «proof».

In most cases, but not always, the proof of theorems has already been found. The theorem applied in architecture and art, expressed by the formula a2+b2 = c2 Pythagorean theorem, and its reverse variant. Famous mathematical theorems are named after their authors who formulated and proved them: Ptolemy, Fermat, Vieta, Ceva, Thales, and others.

In engineering calculations, the most frequently used are both the listed and other theorems related to triangles: cosine, sine, and tangent theorems. Also, theorems about medians, bisectors, the sum of angles in a triangle, etc. Regarding polygons, in theoretical and practical calculations, the theorem about the sum of their angles is in demand. Besides highly important theorems in geometry and other scientific directions, statements designated by terms: lemmas, corollaries, conditions, and propositions are used.