To determine which two segments are most likely parallel, we need to calculate the slopes of the line segments and compare them. If two segments have the same slope, they are parallel.

Step 1: Identify coordinates of endpoints

From the graph:

1. AC: $A(-4, 5)$, $C(-2, 0)$
2. BD: $B(-5, 3)$, $D(-1, -5)$
3. FH: $F(2, 4)$, $H(4, 0)$
4. JG: $J(6, 5)$, $G(3, -2)$

Step 2: Calculate slopes

The formula for slope ($m$) is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

• AC: $m = \frac{0 - 5}{-2 - (-4)} = \frac{-5}{2} = -2.5$

• BD: $m = \frac{-5 - 3}{-1 - (-5)} = \frac{-8}{4} = -2$

• FH: $m = \frac{0 - 4}{4 - 2} = \frac{-4}{2} = -2$

• JG: $m = \frac{-2 - 5}{3 - 6} = \frac{-7}{-3} = \frac{7}{3}$

Step 3: Compare slopes

• AC has a slope of $-2.5$.
• BD and FH both have a slope of $-2$.
• JG has a slope of $\frac{7}{3}$.

Step 4: Conclusion

Since BD and FH have the same slope ($-2$), they are parallel.

Final Answer:

BD and FH

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Related Questions:

1. What is the significance of slope in determining parallelism?
2. How can you calculate the slope if you’re only given a graph?
3. Why are perpendicular lines determined differently from parallel ones?
4. What are real-world applications of identifying parallel lines?
5. How can slopes be calculated from equations in slope-intercept form?

Tip:

When comparing slopes on a graph, calculate carefully to ensure accuracy, as slight errors can lead to incorrect conclusions.