Question

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 corresponding sides of similar triangles are proportional, 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 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.
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Answer 1

The correct response to explain why the slope is the same between any two distinct points on a nonvertical line is:

"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."

This response accurately describes how similar triangles formed from the line have proportional sides, leading to a consistent slope between any two points on the line.