Question

complete the parts below.
(a) find the rise, run, and slope given by triangle abc.
rise: 12 run: 4 slope: 3
(b) find the rise, run, and slope given by triangle def.
rise: 3 run: 1 slope: 3
(c) are the two slopes computed above equal? why or why not?
no. they are not equal because the larger the triangle, the larger the slope.
no. they are not equal because the triangles are similar but not congruent.
yes. they are equal because the two triangles are similar.
yes. they are equal because the two triangles are congruent.

Explanation:

For part (c), we analyze the slopes. The slope of a line is constant for similar triangles because similar triangles have proportional rise and run. Triangle ABC has rise 12, run 4 (slope 12/4 = 3), and triangle DEF has rise 3, run 1 (slope 3/1 = 3). The triangles are similar (proportional sides: 12/3 = 4/1 = 4), so their slopes (rise/run) are equal. The correct reasoning is that similar triangles have proportional rise and run, leading to equal slopes. The option "Yes. They are equal because the two triangles are similar." is correct.

Answer:

Yes. They are equal because the two triangles are similar.