To determine which statement is part of the proof that lines \( l \) and \( n \) have slopes that are opposite reciprocals, we need to analyze the roles that angles and slopes play in this context.
When two lines are perpendicular, the product of their slopes is \(-1\), which means their slopes are opposite reciprocals of each other. The angle information is important here, as it can help establish the relationship between the slopes through right triangles and angle relationships.
Now, let's evaluate the provided options for the proof that involves their slopes:
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△ABC∼△EDA - This asserts that triangle \( ABC \) is similar to triangle \( EDA \). This does not directly relate to the slopes being opposite reciprocals.
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BCCA=−DEAD - This seems to be a statement regarding the relationship of the slopes. However, without context on what \( BCC \) and \( DAE \) refer to (possibly the slopes themselves), it's difficult to validate it directly.
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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. - This option provides specific definitions for the slopes of lines \( l \) and \( n \). If it establishes that one slope is the negative reciprocal of the other, it could be significant.
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∠ABC≅∠DAE - This states that angles \( ABC \) and \( DAE \) are congruent. This fact is essential but is not a definitive proof on its own that relates directly to the slopes being opposite reciprocals.
Based on this analysis, the best choice would be:
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.
This statement includes definitions of the slopes, which is crucial for establishing the relationship needed to show they are opposite reciprocals.