Question

if line 1 is perpendicular to line 2 and line 2 is perpendicular to line 3, then line 1 is parallel to line 3. what is the truth value of this?

Answer 1

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Answer 2

Yeah, this is true. There are many ways to confirm this.

Answer 3

they all are parallel to each other.

Answer 4

1. The slope test. We know that the slope of a line parallel to another is the same and the slope of a line perpendicular is the negative reciprocal. Let's say that the slope of line one is \(x\). What is the slope of line 2? Now, as line 2 is perpendicular to line 3, what is the slope of line 3?

Answer 5

@arris04 Not all... only line 1 and 3.

Answer 6

2. The transversal test. It's known that if the two alternate interior angles add up to 180, then the two lines are parallel and the line that intersects both is a transversal. Do they add up to 180?

Answer 7

Here, line 1 and 3 are the parallels and line 2 is the transversal.

Answer 8

cool, I wanted to confirm my answer. Thanks!~ And the methods you provided are pretty good to support this. ^^