Triangle, Trilateral, Measurement

If Triangle and Trilateral are equivalent, it is only by virtue of Angle being conceived as an intersection of two sides.  But once measurement becomes a factor, there is no interchangeability, e. g. in the famous Pythagorean theorem, which relates the measurements of three sides, there can be no linear substitution for the concept of Right Angle that qualifies it.  Now, Trigonometry establishes a correspondence between linear measurement and angular measurement, but the correspondence is not grounded in a mathematically systematic translation.  Furthermore, there can be no such ground.  For, linear measurement is extensive, i. e. the counting of units that are progressively appended, while angular measurement is intensive, i. e. a subdivision of a whole, usually 360 degrees, an arbitrary quantity.  But that whole is a rotation.  Hence, the angle between any two sides of a Triangle is that between two radii of a Circle, abstracted from the context of the latter.  So, if an Angle is something more that a mere intersection of Lines, Triangle and Trilateral are not equivalent.