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

  • Context: High School 
  • Thread starter Thread starter RuroumiKenshin
  • Start date Start date
Click For Summary
SUMMARY

The discussion centers on the definition of perpendicular lines and their relationship to right angles. It is established that if two lines are perpendicular, they intersect at right angles, regardless of how they may appear from different viewing angles. The confusion arises from the perception of angles, but the mathematical definition remains clear: perpendicular lines are always at right angles. The conversation emphasizes the importance of understanding geometric definitions over visual interpretations.

PREREQUISITES
  • Understanding of basic geometry concepts, specifically angles and lines.
  • Familiarity with the definition of perpendicular lines.
  • Knowledge of how perspective can affect visual perception of angles.
  • Basic understanding of coordinate planes and their representation.
NEXT STEPS
  • Research the properties of perpendicular lines in Euclidean geometry.
  • Explore the concept of angles and their measurement in different contexts.
  • Learn about visual perception and how it can affect the interpretation of geometric figures.
  • Study the implications of Lorentz Transformations on geometry in physics.
USEFUL FOR

This discussion is beneficial for students of geometry, educators teaching mathematical concepts, and anyone interested in the relationship between visual perception and geometric definitions.

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...
 
Mathematics news on Phys.org
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.
 

Similar threads

High School Reprise: Calculate the distance between two points without using a coordinate system
  • · Replies 1 ·
Replies
1
Views
2K
High School Acute Triangle ABC: Point P and Line Intersections Formula
  • · Replies 1 ·
Replies
1
Views
2K
High School Cross section (?) of Great Pyramid from drone footage
  • · Replies 47 ·
2
Replies
47
Views
6K
High School Invariant under rotation: Banal, obvious, or noteworthy?
  • · Replies 2 ·
Replies
2
Views
2K
High School Cartesian Space vs. Euclidean Space
  • · Replies 10 ·
Replies
10
Views
2K
High School Acute Triangle ABC: Proving Perpendicular Lines AD and EF
  • · Replies 1 ·
Replies
1
Views
2K
High School Compensating for a bias - a simple geometry/algebra problem:
  • · Replies 1 ·
Replies
1
Views
2K
Finding acute angle between lines/planes and between planes.
  • · Replies 19 ·
Replies
19
Views
3K
High School Points on a Circle (moving through an obstacle)
  • · Replies 1 ·
Replies
1
Views
1K
High School Defining handedness, right-left, or clockwise-counterclockwise
  • · Replies 3 ·
Replies
3
Views
2K