Let's address the given geometrical problem involving two right triangles, △DEF and △FGH that are similar. As we know, in similar triangles, lengths of corresponding sides stand in the same ratio and they have the same shape, though not necessarily the same size.
A fundamental property of similar triangles is that corresponding angles are congruent and corresponding sides are proportional. This means the ratio of any two corresponding sides in two similar geometric figures is always the same.
We are interested in the slopes of two lines: DF and FH. The term 'slope' refers to the measure of the steepness of a line - defined as the ratio of the vertical change (change in y-values) to the horizontal change (change in x-values).
Since DEF and FGH are similar triangles, the proportional characteristic implies that the slope of line DF will be equal to the slope of line FH. This is because the ratio of the vertical to the horizontal change in both these lines will be the same due to the proportionality of the triangles' corresponding sides.
Hence we can say that the slope of DF is equal to the slope of FH. It's a direct relation due to the similarity of the triangles. There is no calculation performed in this deduction; it's purely the application of the fundamental concept of similar triangles. So, essentially in similar triangles, the corresponding sides not only have the same ratio of lengths but the lines containing these sides also have the same slope.