Incidence
Theorem (Line Uniqueness) If
and
belong to line
and
then
![incidence _gr_5.gif]](pages/incidence/Images/incidence_gr_5.gif)
Proof.
We will use a direct proof.
Theorem (How Lines and Planes Meet) (i) If two distinct lines
and
meet, their intersection is a single point.
(ii) If a line meets a plane and is not contained by that plane, their intersection is a point.
Proof.
We will use the indirect proof method for (i) as follows:
![incidence _gr_9.gif]](pages/incidence/Images/incidence_gr_9.gif)
We will also use the indirect proof method for (ii) as follows:
![incidence _gr_10.gif]](pages/incidence/Images/incidence_gr_10.gif)
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Cite this as: Incidence Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/incidence.html
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