In this paper, it is shown that the Fibonacci triangle is formed from the elements of power transformations of a quadratic trinomial. It is binary structured by domains of rows of equal lengths, in which the sum of numbers forms a sequence of certain numbers. This sequence coincides with the transformed bisection of the classical sequence of Fibonacci numbers. The paper substantiates Pascal's rule for calculating elements in the lines of a Fibonacci triangle. The general relations of two forgings of numbers in lines of a triangle of Fibonacci for arbitrary values are received