Drag statements and reasons to each row to show why the slope of the line between D and E is the same as the slope between E and F, given that triangles A and B are similar.

To show why the slope of the line between points D and E is the same as the slope between points E and F, given that triangles A and B are similar, let’s break it down step by step:

1. Definition of slope: The slope is defined as the ratio of the change in the y-values (rise) to the change in the x-values (run) between any two points on a line.

2. 4/3 = 16/12: This represents a proportion showing that the ratio of the vertical change to the horizontal change is the same for both segments, which confirms that the slopes are equal.

3. 4 – 3 = 16 – 12: This is an algebraic verification that the differences (or changes) in y-values and x-values are consistent between the two triangles, aligning with the slope definition.

4. Triangle A is similar to Triangle B: Because triangles A and B are similar, the ratios of corresponding sides (and thus their slopes) are the same. This similarity ensures that the slopes calculated from points D to E and E to F will match.

5. The area of triangle A is greater than the area of triangle B: This statement is not directly related to the equality of the slopes, so it doesn’t contribute to the understanding of the slopes between the line segments.

In summary, the correct statements to connect would be:

– Triangle A is similar to Triangle B. (to establish proportionality)