Abstract: 
This entry contains a definition of angles between vectors and between three
points. Building on this, we prove basic geometric properties of triangles, such
as the Isosceles Triangle Theorem, the Law of Sines and the Law of Cosines, that
the sum of the angles of a triangle is π, and the congruence theorems for
triangles.
The definitions and proofs were developed following those by John Harrison in
HOL Light. However, due to Isabelle's type class system, all definitions and
theorems in the Isabelle formalisation hold for all real inner product spaces.

BibTeX: 
@article{TriangleAFP,
author = {Manuel Eberl},
title = {Basic Geometric Properties of Triangles},
journal = {Archive of Formal Proofs},
month = dec,
year = 2015,
note = {\url{http://isaafp.org/entries/Triangle.shtml},
Formal proof development},
ISSN = {2150914x},
}
