Q:

# What does the intersection of two planes create?

A:

In geometry, the intersection of two planes forms a line. This is one of the basic postulates put forth by Euclid in his geometry treatise of 13 books called "Elements". Postulates in geometry are basic assumptions that are generally accepted without requiring proof.

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Planes and lines are both composed of points, which are the most fundamental units in geometry. Points represent a single position and mathematicians regard them as dimensionless. They are customarily referred to with a single capital letter, such as A or B.

A line is a one-dimensional set of points that goes off to infinity in two opposing directions. Lines have length but not width or height. They are typically represented using any two points that lie along the line. The intersection of two lines in a plane is a single point. If two lines lie in the same plane but do not intersect, those lines are parallel to each other.

A plane is a two-dimensional set of points that has length and width but no height. A plane forms a flat surface that goes off to infinity in all directions along the surface. Planes are represented using three points in the plane that are not on the same line. These are noncollinear points.

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