Why can you use similar triangles to explain why the slope is the same between any two distinct points on a nonvertical line?(1 point) Responses The hypotenuses of similar triangles used at different points along the line form the slope of the line. A ratio can be created from the hypotenuses of two similar triangles to calculate the slope of that line. The hypotenuses of similar triangles used at different points along the line form the slope of the line. A ratio can be created from the hypotenuses of two similar triangles to calculate the slope of that line. In similar triangles, the change in y-values represents the run, and the change in x-values represents the rise of the line the triangles are placed against. So the ratio riserun can show that the slope is the same between any two points along the line. In similar triangles, the change in y -values represents the run, and the change in x -values represents the rise of the line the triangles are placed against. So the ratio Start Fraction rise over run End Fraction can show that the slope is the same between any two points along the line. The legs of similar triangles used at different points along the line represent the rise and run of the line, or its slope. The corresponding sides of similar triangles are proportional, so the slope can be shown as the same using any two points along the line. The legs of similar triangles used at different points along the line represent the rise and run of the line, or its slope. The

Question

Why can you use similar triangles to explain why the slope is the same between any two distinct points on a nonvertical line?(1 point) Responses The hypotenuses of similar triangles used at different points along the line form the slope of the line. A ratio can be created from the hypotenuses of two similar triangles to calculate the slope of that line. The hypotenuses of similar triangles used at different points along the line form the slope of the line. A ratio can be created from the hypotenuses of two similar triangles to calculate the slope of that line. In similar triangles, the change in y-values represents the run, and the change in x-values represents the rise of the line the triangles are placed against. So the ratio riserun can show that the slope is the same between any two points along the line. In similar triangles, the change in y -values represents the run, and the change in x -values represents the rise of the line the triangles are placed against. So the ratio Start Fraction rise over run End Fraction can show that the slope is the same between any two points along the line. The legs of similar triangles used at different points along the line represent the rise and run of the line, or its slope. The corresponding sides of similar triangles are proportional, so the slope can be shown as the same using any two points along the line. The legs of similar triangles used at different points along the line represent the rise and run of the line, or its slope. The

Answer 1

The legs of similar triangles used at different points.. is the right answer btw!

Answer 2

corresponding sides of similar triangles are proportional, so the slope can be shown as the same using any two points along the line.

Answer 3

The answer is?

Answer 4

The answer is: The corresponding sides of similar triangles are proportional, so the slope can be shown as the same using any two points along the line.

Answer 5

Apologies for the incorrect response. You are correct. The correct answer is: The legs of similar triangles used at different points along the line represent the rise and run of the line, or its slope.

Answer 6

corresponding sides of similar triangles are proportional. This means that if we have two similar triangles, the ratios of their corresponding sides will be equal.

To explain why the slope is the same between any two distinct points on a nonvertical line using similar triangles, we can consider two points A and B on the line. We can then create two right triangles by connecting each point to a third point C on the line (where C has the same x-coordinate as A and the same y-coordinate as B).

These two right triangles will be similar because they share an angle and have a pair of proportional sides. Specifically, the sides opposite the shared angle (the legs of the triangles) will be proportional.

Now, let's consider the change in the y-values (rise) and the change in the x-values (run) between points A and B. In the similar triangles, the change in y-values represents the run, and the change in x-values represents the rise of the line that the triangles are placed against.

The ratio of the rise to the run can be calculated as the ratio of the lengths of the corresponding legs of the similar triangles. Since the corresponding sides of similar triangles are proportional, this ratio will be the same for any two points on the line.

In other words, by comparing the lengths of the legs of the similar triangles, we can calculate the ratio of the rise to the run, which gives us the slope of the line. This shows that the slope is the same between any two points on the line.

So, using similar triangles, we can see that the hypotenuses (the ratios of the rise to the run) of the triangles used at different points along the line form the slope of the line.