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
Bernoulli's triangle component in row "n" and column "k", then: As in Pascal's triangle and other similarly constructed triangles, sums of components along diagonal paths in Bernoulli's triangle result in the Fibonacci numbers. Bernoulli's triangle Bernoulli's triangle is an array of partial sums of the binomial coefficients. For any non-negative integer "n" and for any integer "k" included between 0 and "n", the component in row "n" and column "k" is given by: i.e., the sum of the first "k" "n"th-order binomial coefficients. The first rows of Bernoulli's triangle are: Similarly to Pascal's triangle, each component of Bernoulli's triangle is the sum