Question

Given that lines l and n are perpendicular, which of the following is part of the proof that l and n have slopes that are opposite reciprocals? (1 point) Responses The slope of line l is BCCA and the slope of line n is DEAD . The slope of line l is cap b cap c over cap c cap A and the slope of line n is cap d cap e over cap A cap d. BCCA=−DEAD cap b cap c over cap c cap A is equal to negative cap d cap e over cap A cap d ∠ABC≅∠DAE ∠ABC≅∠DAE △ABC∼△EDA

Answer 1

To show that lines \( l \) and \( n \) are perpendicular, we need to demonstrate that their slopes are opposite reciprocals.

Given your provided options, we can focus on how to establish the relationship between the angles formed by these lines. The crucial part of a proof involves showing that the angles formed when two lines are perpendicular are congruent, thereby allowing us to relate their slopes.

One key part of the proof that \( l \) and \( n \) are perpendicular can be summarized as follows:

• If \(\angle ABC \cong \angle DAE\), then the slopes can be shown to be opposite reciprocals because these angles correspond to angles formed by the lines.
• Hence, expressing this congruence can lead to the conclusion that the slopes \( m_1 \) and \( m_2 \) of the lines satisfy \( m_1 = -\frac{1}{m_2} \).

Among the provided statements, \( \angle ABC \cong \angle DAE \) would be a crucial part of the proof since it indicates the relationship necessary to prove that the lines are perpendicular, leading us to the conclusion about their slopes.

So the relevant response is: \( \angle ABC \cong \angle DAE \).