Are Perpendicular Lines Always Right Angles, Even if They Appear Acute?

  • Context: High School 
  • Thread starter Thread starter RuroumiKenshin
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Discussion Overview

The discussion revolves around the nature of perpendicular lines and whether they can appear acute from certain perspectives. Participants explore the definitions of perpendicularity and right angles, as well as the implications of visual perception on geometric relationships.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions whether lines that appear acute can still be considered perpendicular, suggesting a need for a more substantiated answer.
  • Another participant asserts that if two lines are perpendicular, they intersect at right angles, but challenges the assumption of their perpendicularity based on appearance.
  • A different participant references the definition of perpendicular angles as right angles, raising the question of relativity in perception.
  • One participant expresses frustration at the introduction of relativity, emphasizing that perpendicular lines are defined as crossing at right angles.

Areas of Agreement / Disagreement

Participants express disagreement regarding the interpretation of perpendicularity and the influence of perspective on geometric definitions. There is no consensus on whether visual perception can alter the understanding of perpendicular lines.

Contextual Notes

The discussion highlights the potential for confusion between the definitions of angles and lines, as well as the impact of perspective on geometric interpretation. Some assumptions about visual perception and definitions remain unresolved.

RuroumiKenshin
The other day, I was looking at two intersecting straight lines. They were drawn from a certain angle so that they looked acute. But if you sort of changed the angle of your view (by turning the paper a bit to the side), it looked like, quite simply, a coordinate plane without a graph. So, since the two lines where perpendicular to each other, does it mean they are right angles? Even if they only look acute?
My sister and I had quite a bit of a quarrel over this...and I wanted an answer that was more substantiated, or rather "standard" so that more people could agree. Okay, so bring it on...
 
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HallsofIvy

The other day, I was looking at two intersecting straight lines. They were drawn from a certain angle so that they looked acute. But if you sort of changed the angle of your view (by turning the paper a bit to the side), it looked like, quite simply, a coordinate plane without a graph. So, since the two lines where perpendicular to each other, does it mean they are right angles? Even if they only look acute?/QUOTE]

I'm not sure I understand your question. Certainly if two lines ARE perpendicular, then they cross at right angles. (On the other hand, no, "they" are NOT right angles because lines are not angles!)

How do you KNOW they are perpendicular if they LOOK acute?
 
uhh...that was my question.
By definition, perpendicular angles are right angles right?

or is the whole situation relative? (i personally don't believe so)
 
I don't think I follow what you say completely. Angle is a relative quantity due to Lorentz Transformations, and the way space changes while traveling at different speeds. But yeah, I don't think that was quite what you were asking.
 
Oh, for God's sake don't bring relativity into it!


Yes, "perpendicular" means "at right angles".

Two lines are perpendicular if and only if they cross at right angles.
 

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