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Drag statements and reasons to each row to show why the slope of the line between R and S is the same as the slope between S and T, given that triangles A and B are similar.
Definition of slope
5 – 3 = 15 – 9
5/3 = 15/9
The area of triangle A is greater than the area of triangle B.
5/3 = slope
To explain why the slope of the line between R and S is the same as the slope between S and T, given that triangles A and B are similar, let’s break it down step by step:
1. Definition of slope: Slope is defined as the change in the y-coordinates divided by the change in the x-coordinates (rise over run).
2. Using the values: From the relationship provided, ( frac{5}{3} = frac{15}{9} ), this means the slope from R to S (which corresponds to triangle A) is equal to the slope from S to T (which corresponds to triangle B). This indicates a consistent rise over run across both triangles since triangles A and B are similar.
3. Similar triangles: Since triangles A and B are similar, their corresponding side lengths are in proportion. This means that the ratios of the rises and runs between the points (which correspond to the sides of the triangles) will be equal.
Thus, the final arrangement for the statements and reasons could be:
– Row for Definition of slope: “Slope is the change in y over change in x.”
– Row for 5 – 3 = 15 – 9: “Calculates the differences in y-coordinates.”
– Row for 5/3 = 15/9: “Shows that the slopes are equal.”
– Row for Similar triangles: “Triangles A