How many planes can pass through
three noncolinear points?
Imagine that we have three
arbitrary points in space 𝐴, 𝐵, and 𝐶. We know that between any two
points, there exists only one line, which means one line passes through the point
𝐴𝐵; one line could pass through the point 𝐴𝐶, which would create a set of
intersecting lines. And if there wasn’t a line passing
from the point 𝐴𝐶, if the line through 𝐶 is parallel to the line 𝐴𝐵, it is
still true that 𝐴, 𝐵, and 𝐶 are noncolinear. They’re not on the same line. But parallel lines in space and
intersecting lines in space are coplanar; they exist on the same plane. And this means that through any
three non colinear points, there will be exactly one plane.
Based on the properties of points,
lines, and planes in space, we can say that there exists exactly one plane through
any three noncolinear points.