Geometry question (not homework)

  • Context: High School 
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    Geometry Homework
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Discussion Overview

The discussion revolves around the geometric properties of planes, particularly their intersections. Participants explore whether multiple planes can intersect a given plane at a line and the implications of such intersections in different configurations.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions if planes can only rise or dip or if they can intersect in a more complex manner.
  • Another participant provides an example of planes intersecting at right angles, referencing the intersection of the xy-plane with the xz-plane.
  • A participant mentions a class problem suggesting that through a given line on one plane, only one plane can intersect another, expressing confusion over this claim.
  • Another participant suggests that rotating a plane around the line of intersection would yield an infinite number of planes intersecting the second plane.
  • One participant asserts their teacher's claim that only one plane intersects another through a given line, seeking clarification.
  • Another participant questions if the teacher meant that any two given planes can only intersect once, suggesting this interpretation makes more sense.
  • One participant argues that there should be infinite planes intersecting with the first plane, noting that only parallel planes do not intersect.
  • A participant expresses uncertainty about their teacher's assertion, indicating a belief that the teacher might be incorrect.

Areas of Agreement / Disagreement

Participants express disagreement regarding the number of planes that can intersect another plane through a given line. Some support the idea of only one plane intersecting, while others argue for the existence of multiple intersecting planes.

Contextual Notes

There are unresolved assumptions regarding the conditions under which planes intersect, particularly concerning the definitions of intersection and the specific configurations being discussed.

Someone502
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can planes only rise up or dip down like this?


/ Plane B
/
/
/
/

_____________________________ Plane A

or can Plane B intersect A like this?
_____________________________________
|BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB|
|BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB|
|BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB|
|BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB|
|BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB|
|BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB|
|_____________________________________|___ Plane A
|BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB|
|_____________________________________|

bad drawing but i don't know any other way.
 
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If your drawing is referring to planes intersecting at right angles, the most apparent example is the intersection of the xy-plane with the xz-plane.
 
We had a problem in class that said that through a given line on plane A there is only one plane that intersects plane B (not dealing with my pictures). I thought there would be an infinite amount of planes.
 
Someone502 said:
We had a problem in class that said that through a given line on plane A there is only one plane that intersects plane B (not dealing with my pictures). I thought there would be an infinite amount of planes.

Was there more to the problem? Imagine rotating the plane around the line where it intersects A. That will give an infinite number of planes that still intersect B.
 
my teacher said that there was only one and that's what I am asking about.
 
opps and the plane that intersects plane B pass through the line.
 
Are you sure he didn't say any two given planes can only intersect once? because that would make a lot more sense.
 
no pretty sure
 
Well there should be infinite planes (B) that intersect with A. Just think about it. In fact, only planes which are parallel to each other won't intersect.
 
  • #10
ok my teacher said there was only one and i thought he was wrong but wasnt sure
 

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