Question

question 1 of 15 (1 point) | question attempt: 1 of 5
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?

Explanation:

Step 1: Determine coordinates of points for triangle ABC

From the graph, point B is at (0, 1) and point A is at (12, 1), point C is at (12, 10).

• Rise for triangle ABC: vertical change from A to C, so \( 10 - 1 = 9 \).
• Run for triangle ABC: horizontal change from B to A, so \( 12 - 0 = 12 \).
• Slope is \( \frac{\text{rise}}{\text{run}} = \frac{9}{12} = \frac{3}{4} \).

Step 2: Determine coordinates of points for triangle DEF

Point E is at (4, 4), point D is at (8, 4), point F is at (8, 7).

• Rise for triangle DEF: vertical change from D to F, so \( 7 - 4 = 3 \).
• Run for triangle DEF: horizontal change from E to D, so \( 8 - 4 = 4 \).
• Slope is \( \frac{\text{rise}}{\text{run}} = \frac{3}{4} \).

Step 3: Compare slopes

The slope of ABC is \( \frac{3}{4} \) and slope of DEF is \( \frac{3}{4} \), so they are equal because they lie on the same line (parallel triangles, same line means same slope).

Part (a)

• Rise: \( 9 \)
• Run: \( 12 \)
• Slope: \( \frac{3}{4} \)

Part (b)

• Rise: \( 3 \)
• Run: \( 4 \)
• Slope: \( \frac{3}{4} \)

Part (c)

Yes, the two slopes are equal because triangles ABC and DEF are similar (they lie on the same straight line), so their rise over run ratios (slopes) are equal.

Answer:

s:
(a) rise: \( \boldsymbol{9} \), run: \( \boldsymbol{12} \), slope: \( \boldsymbol{\frac{3}{4}} \)
(b) rise: \( \boldsymbol{3} \), run: \( \boldsymbol{4} \), slope: \( \boldsymbol{\frac{3}{4}} \)
(c) Yes, because both triangles lie on the same line, so their slopes (rise/run) are equal.