Question

4.4 parallel and perpendicular lines quiz

two parallel lines always have the same slope.
true
false

Explanation:

Analyze the definition of parallel lines

Using the Parallel Lines Slopes knowledge point

$$ \text{Parallel lines are lines in the same plane that never intersect.} $$

Examine the slopes of non-vertical parallel lines

Using the Parallel Lines Slopes knowledge point

$$ y = m_1x + b_1 \quad \text{and} \quad y = m_2x + b_2 \implies m_1 = m_2 $$

Consider vertical lines as a special case

Using the Slope of Vertical Lines knowledge point

$$ x = c_1 \quad \text{and} \quad x = c_2 \implies \text{Slopes are undefined} $$

Evaluate the statement

Since vertical lines are parallel but their slopes are undefined, they do not have a numerical slope. Thus, they do not "have the same slope" because their slope does not exist. Therefore, the statement is not always true.

Answer:

• True
• (B) False (Correct answer)