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
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 interior angles of similar triangles used at different points along the line can be added to measure the slope of the line. The corresponding angles of similar triangles are the same, so the slope can be shown as the same using any two points along the line.
The interior angles of similar triangles used at different points along the line can be added to measure the slope of the line. The corresponding angles of similar triangles are the same, 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 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 corresponding sides of similar triangles are proportional, so the slope can be shown as the same using any two points along the 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.
the correct answer was: 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 corresponding sides of similar triangles are proportional, so the slope can be shown as the same using any two points along the line.
bot your incorrect
The correct explanation is: "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 rise/run can show that the slope is the same between any two points along the line."
To understand why this is the case, let's break it down step by step.
1. Start with two distinct points on a nonvertical line. We want to show that the slope between these two points is the same, regardless of which points we choose.
2. Create two right triangles using these two points as vertices. The first triangle has one leg parallel to the x-axis (change in x-values) and one leg parallel to the y-axis (change in y-values).
3. Now, take another pair of distinct points on the line and create a second right triangle using those points as vertices. This triangle will have the same properties as the first one, with one leg parallel to the x-axis and one leg parallel to the y-axis.
4. Since the triangles are similar (meaning they have the same shape but possibly different sizes), their corresponding sides are proportional. This means that the ratio of the change in y-values to the change in x-values is the same for both triangles.
5. In terms of slope, the change in y-values represents the rise of the line, and the change in x-values represents the run. So, the ratio rise/run (or change in y-values/change in x-values) is equal for both triangles.
6. Since the ratio is equal for any two points on the line, we can conclude that the slope is the same between any two distinct points on a nonvertical line.
So, by using similar triangles and considering the ratio of rise over run, we can explain why the slope is the same between any two distinct points on a nonvertical line.