Question

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 similar triangles can have different sizes.
no. they are not equal because the larger the triangle, the smaller the slope.

Explanation:

Step1: Determine rise and run for triangle ABC

Rise is the vertical change. For triangle ABC, rise = 2. Run is the horizontal change. For triangle ABC, run = 3.
Slope formula is \(m=\frac{\text{rise}}{\text{run}}\). So slope of \(ABC=\frac{2}{3}\)

Step2: Determine rise and run for triangle DEF

For triangle DEF, rise = 4. Run = 6.
Slope of \(DEF=\frac{4}{6}=\frac{2}{3}\) (simplified by dividing numerator and denominator by 2)

Answer:

(a) rise: 2, run: 3, slope: \(\frac{2}{3}\)
(b) rise: 4, run: 6, slope: \(\frac{2}{3}\)
(c) Yes. They are equal because the two triangles are similar.