Question

complete the parts below.
(a) find the run, rise, and slope given by triangle abc.
run: rise: slope:
(b) find the run, rise, and slope given by triangle def.
run: rise: 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 larger the triangle, the larger the slope.
no. they are not equal because the smaller the triangle, the smaller the slope.

Explanation:

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

The run is the horizontal change. Counting the grid - squares from $C$ to $B$, run = 4. The rise is the vertical change. Counting the grid - squares from $B$ to $A$, rise = 3. The slope $m=\frac{\text{rise}}{\text{run}}$, so $m=\frac{3}{4}$.

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

The run is the horizontal change. Counting the grid - squares from $F$ to $E$, run = 8. The rise is the vertical change. Counting the grid - squares from $E$ to $D$, rise = 6. The slope $m=\frac{\text{rise}}{\text{run}}=\frac{6}{8}=\frac{3}{4}$.

Step3: Compare the slopes

The slopes of the two lines (represented by the two triangles) are equal because the two triangles are similar. For similar right - triangles formed by a line, the ratio of rise to run (slope) is the same.

Answer:

(a) run: 4
rise: 3
slope: $\frac{3}{4}$
(b) run: 8
rise: 6
slope: $\frac{3}{4}$
(c) Yes. They are equal because the two triangles are similar.