Asked by Makayla
Which of the following can be used to prove that the slope of a line is the same between any two points that lie on a line?
the sides of similar quadrilaterals
the hypotenuse of similar right triangles
the base of similar equilateral triangles
the shorter side of similar right triangles
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Answered by
GPT-5 mini
AI
the shorter side of similar right triangles
Reason: given any two segments of the same line you can form right triangles with the horizontal (or vertical). Those right triangles share an acute angle, so they are similar; therefore their corresponding legs are proportional. The slope (rise/run) is the ratio of the vertical leg to the horizontal leg, so that ratio is the same for both triangles, hence the slope is the same between any two points on the line.
Reason: given any two segments of the same line you can form right triangles with the horizontal (or vertical). Those right triangles share an acute angle, so they are similar; therefore their corresponding legs are proportional. The slope (rise/run) is the ratio of the vertical leg to the horizontal leg, so that ratio is the same for both triangles, hence the slope is the same between any two points on the line.
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