Exterior angle theorem sum of angles of a triangle is 180°. If it is known that the sum of the measures of the angles in a triangle is 180°, then the HSEAT is proved as follows: On the other hand, if the HSEAT is taken as a true statement then: Proving that the sum of the measures of the angles of a triangle is 180°. The Euclidean proof of the HSEAT (and simultaneously the result on the sum of the angles of a triangle) starts by constructing the line parallel to side "AB" passing through point "C" and then using the properties of
Skinny triangle based on the small-angle approximations; and, when formula_5 is in radians. The proof of the skinny triangle solution follows from the small-angle approximation by applying the law of sines. Again referring to figure 1; The term formula_7 represents the base angle of the triangle and is this value because the sum of the internal angles of any triangle (in this case the two base angles plus "θ") are equal to "π". Applying the small angle approximations to the law of sines above results in; the desired result. This result is equivalent to assuming that the length of the base of