Use the diagram and given information to answer the 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.
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.
Just for yall in the future ;)
I'm stuck on this question right now and I don't even know where to start...
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.
The correct description that shows that lines l and m have slopes that are opposite reciprocals is:
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.
To understand why, we need to know that for two lines to be perpendicular, their slopes must be opposite reciprocals of each other. In this case, we are given that lines l and m are perpendicular. Therefore, to prove that their slopes are opposite reciprocals, we need to show that the corresponding sides of the similar triangles have equal ratios.
In the given information, it says that △ABC ∼ △CDE, which means that the corresponding angles in the two triangles are equal, and the corresponding sides are proportional. Specifically, we are told that AB is vertical, and ED is also vertical, which means they are corresponding sides in the similar triangles.
From the similar triangles, we are given that ABBC = CDDE, which means that the ratio of AB to BC is equal to the ratio of CD to DE. We can write this as:
AB/BC = CD/DE
Now, we know that slope is defined as the ratio of the vertical change to the horizontal change. The slope of line l is the vertical change (AB) divided by the horizontal change (BC), so it's AB/BC. Similarly, the slope of line m is CD/DE.
Therefore, based on the given information and the similar triangles, we can conclude that the slope of line l is −BCAB and the slope of line m is CDDE. Since ABBC and −BCAB are opposite reciprocals (their product is -1) and CDDE is the reciprocal of ABBC, we can say that lines l and m have slopes that are opposite reciprocals.