In short, theorems.
In the greater sense it proves a conclusion that has been suspected. Given a geometric diagram it can prove new facts about the lengths of lines, values of angles, and relationships between points, lines, angles, and polygons.
For example, given a 30-60-90 triangle a person can find the proportion of the side lengths by using the 30-60-90 triangle proof.
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that is a thereom
A Postulate,
postulates
Theroems
Proven is the past participle; proving is the present participle.