Question

line l is shown below. right triangles abc and def are drawn to measure the slope of the line. complete the parts below. (a) find the rise, run, and slope given by triangle abc. rise: run: slope: (b) find the rise, run, and slope given by triangle def. rise: run: slope: (c) are the two slopes computed above equal? why or why not? yes, they are equal because the two triangles are similar. yes, they are equal because the two triangles are congruent. no, they are not equal because the two triangles are not similar. no, they are not equal because the two triangles are not congruent.

Explanation:

Step1: Find rise, run and slope for triangle \(ABC\)

From the graph, for triangle \(ABC\), the vertical change (rise) is \(2\) units and the horizontal change (run) is \(2\) units.
Using the slope formula \(m=\frac{\text{rise}}{\text{run}}\), we have \(m = \frac{2}{2}\)

Step2: Find rise, run and slope for triangle \(DEF\)

For triangle \(DEF\), the vertical change (rise) is \(4\) units and the horizontal change (run) is \(4\) units.
Using the slope formula \(m=\frac{\text{rise}}{\text{run}}\), we have \(m=\frac{4}{4}\)

Step3: Compare the slopes

Since \(\frac{2}{2}=1\) and \(\frac{4}{4} = 1\)

Answer:

(a) rise: \(2\), run: \(2\), slope: \(1\)
(b) rise: \(4\), run: \(4\), slope: \(1\)
(c) Yes. They are equal because the slope formula \(m=\frac{\text{rise}}{\text{run}}\) gives the same value for both triangles (both slopes equal \(1\))