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To find the **run**, **rise**, and **slope** for triangle \( DEF \), we need the coordinates of points \( D \), \( E \), and \( F \), or at least the specific measurements of the triangle’s vertical (rise) and horizontal (run) distances.

Here’s a general approach for each element:

1. **Run**: This is the horizontal distance, typically calculated as the difference in the \( x \)-coordinates of points \( D \) and \( E \) (or the corresponding points forming the horizontal side of the triangle).
2. **Rise**: This is the vertical distance, calculated as the difference in the \( y \)-coordinates of points \( D \) and \( F \) (or the points forming the vertical side).
3. **Slope**: The slope is the ratio of the rise to the run. Mathematically, \( \text{slope} = \frac{\text{rise}}{\text{run}} \).

If you have coordinates or measurements available, please share them, or if there are any additional images with labeled values, upload them so I can provide exact values for the run, rise, and slope.

Would you like more details on how these calculations are performed?

Here are some related questions:
1. What are the coordinates or measurements of points \( D \), \( E \), and \( F \)?
2. How do you calculate the slope between two points on a coordinate plane?
3. What is the significance of a positive or negative slope in geometry?
4. How does the slope relate to the angle of inclination in a right triangle?
5. What happens to the slope if the run is zero?

**Tip:** When calculating slope, remember that it describes the direction and steepness of a line: a positive slope means an upward incline, while a negative slope indicates a downward incline.

Find the run, rise, and slope given by triangle DEF.

Learn how to find the run, rise, and slope of triangle DEF using coordinate geometry. This problem explores the concepts of horizontal and vertical distances (run and rise) and calculates the slope using these values. Suitable for students in Grades 8-10.

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