Triangle KLM and triangle PRS are similar right triangles. Which proportion can be used to show that the slope of line segment \( \overline{KM} \) is equal to the slope of line segment \( \overline{PS} \)?

Question

09-12-2023
Mathematics

High School

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Triangle KLM and triangle PRS are similar right triangles. Which proportion can be used to show that the slope of line segment \( \overline{KM} \) is equal to the slope of line segment \( \overline{PS} \)?

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aditigupte1 aditigupte1 · Answer 1 · 2023-09-17T14:21:46-04:00

The proportion that can be used to show that the slope of bar KM is equal to the slope of bar PS is the ratio of their vertical changes to their horizontal changes.

To find the slope of a line, we need to calculate the ratio of the vertical change (rise) to the horizontal change (run). In this case, since triangles KLM and PRS are similar right triangles, their corresponding sides are proportional. Therefore, we can use the ratio of the lengths of corresponding sides to find the proportion of their slopes.

To show that the slope of bar KM is equal to the slope of bar PS, we can use the concept of similar triangles. Since triangles KLM and PRS are similar right triangles, their corresponding sides are proportional. This means that the ratio of the lengths of corresponding sides in the triangles will be the same.

To find the slope of a line, we calculate the ratio of the vertical change (rise) to the horizontal change (run). Therefore, the proportion that can be used to show the equality of slopes is the ratio of the vertical changes (corresponding side lengths) to the horizontal changes (corresponding side lengths) in the triangles.

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