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Parallel Planes and Lines - Problem 1

Teacher/Instructor Brian McCall
Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

The intersection of two planes is a line. If the planes do not intersect, they are parallel. They cannot intersect at only one point because planes are infinite. Furthermore, they cannot intersect over more than one line because planes are flat. One way to think about planes is to try to use sheets of paper, and observe that the intersection of two sheets would only happen at one line. The intersection of planes happens in a three-dimensional space.

A common question when you are learning about planes in geometry is what is the intersection of two planes?

Well you can think of a plane as a sheet of paper. So here we are talking about what if you had two sheets of paper intersecting each other? Well the first thing in this is about it doesn’t matter what angle this two planes intersect is that going to affect what happens. Well as long as they are not parallel that is where two planes will never intersect, if I can hold this perfectly parallels. This would be parallel planes.

If I took one of these I see that they are going to intersect and that intersection would be along this line right here. So these planes which extend infinitely in their directions would create an intersection of a line.

So the intersection of two planes will be a line. You can use this concept when you think about a plane intersecting different three dimensional solids.

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