Question regarding angles

B

bilius2007

New member
Joined
Dec 9, 2020
Messages
20
In my school notes, they defined an angle as two noncollinear rays called sides. But can't collinear rays form 180 degree angles?
 

Attachments

  • Angle.png
    Angle.png
    413.1 KB · Views: 6
bilius2007 said:
In my school notes, they defined an angle as two noncollinear rays called sides. But can't collinear rays form 180 degree angles?
Click to expand...
In Euclidean geometry,

an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.​

Angles formed by two rays lie in the plane that contains the rays.

Angles are also formed by the intersection of two planes. These are called dihedral angles. Wikipedia
 
bilius2007 said:
In my school notes, they defined an angle as two noncollinear rays called sides. But can't collinear rays form 180 degree angles?
Click to expand...
Actually, it really depends upon who is writing the definitions. Most advanced courses is axiomatic geometry textbooks define an angle as the union of two rays with a common end point. However, one of the most important mathematicians of the late century, RL Moore, used the definition that you posted. So it is not correct to say that your notes are wrong as two others have done. You must follow the definitions in your own text material. Just be aware that there are disagreements as to definitions.
 
bilius2007 said:
In my school notes, they defined an angle as two noncollinear rays called sides. But can't collinear rays form 180 degree angles?
Click to expand...
One reason they would use their definition (in their context) is that for a 180 degree angle you can't distinguish interior and exterior! Also, probably some theorems they state would not apply.
 
As long as you know what an angle is I would not worry about this, although I like that this bothers you!
 
You must log in or register to reply here.
Top