Use the diagram and given information to answer the question.

Question

Lines l and m intersect at point C. More information is in the long description.
.Long Description: Image of Lines
Given: △ABC∼△CDE
BC⎯⎯⎯⎯⎯⎯⎯⎯ and CD⎯⎯⎯⎯⎯⎯⎯⎯ are horizontal segments.
AB⎯⎯⎯⎯⎯⎯⎯ and ED⎯⎯⎯⎯⎯⎯⎯⎯ are vertical segments.
Lines l and m are perpendicular.
Prove: Lines l and m have slopes that are opposite reciprocals.
What description shows that lines l and m have slopes that are opposite reciprocals?
The triangles are similar, so BCAB=DECD. The slope of l=BCAB and the slope of m=−CDDE. Since DECD and −CDDE are opposite reciprocals, lines l and m have slopes that are opposite reciprocals.
The triangles are similar, so ABBC=CDDE. The slope of l=−BCAB and the slope of m=CDDE. Since ABBC and −BCAB are opposite reciprocals, lines l and m have slopes that are opposite reciprocals.
The triangles are similar, so ABBC=CDDE. The slope of l=ABBC and the slope of m=−DECD. Since CDDE and −DECD are opposite reciprocals, lines l and m have slopes that are opposite reciprocals.
The triangles are similar, so BCAB=DECD. The slope of l=−ABBC and the slope of m=DECD. Since BCAB and −ABBC are opposite reciprocals, lines l and m have slopes that are opposite reciprocals.

Answer 1

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Answer 2

Since similar triangles have proportional sides, use the proportion BCAB=DECD. Show that the slope of l=DECD and the slope of m=−ABBC. Then show that BCAB(−ABBC)=−1, so the slopes of l and m are opposite reciprocals.

Answer 3

The correct answer is I
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The triangles are similar, so AB/BC=CD/DE. The slope of l=AB/BC and the slope of m=−DE/CD. Since CDDE and −DE/CD are opposite reciprocals, lines l and m have slopes that are opposite reciprocals.

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