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Incidence

Theorem (Line Uniqueness) If incidence _gr_1.gif] and incidence _gr_2.gif] belong to line incidence _gr_3.gif] and incidence _gr_4.gif] then incidence _gr_5.gif]

    Proof. We will use a direct proof.
    
incidence _gr_6.gif]

Theorem (How Lines and Planes Meet) (i) If two distinct lines incidence _gr_7.gif] and incidence _gr_8.gif] 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]

We will also use the indirect proof method for (ii) as follows:
    
incidence _gr_10.gif]
incidence _gr_11.gif]

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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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