Question
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.
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.
Answers
Anakin Skywalker
I'm stuck on this question right now and I don't even know where to start...
your welcome
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.
DASYAHH!
The correct answer is I
v
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 ;)
v
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 ;)