63 Theorems on Lines and Planes
A)
Postulate 47 review
a.
Postulate 4 (The Line Postulate)
i.
For every 2 points there is exactly one line that contains
both points
b.
Postulate 5
i.
Every plane contains at least three noncollinear points
ii.
Space contains at least four noncoplanar points
c.
Postulate 6
i.
If two points of a line lie in a plane, then the line lies in
the same plane
d.
Postulate 7
i.
Any three points lie in at least one plane, and any three
noncollinear points lie in exactly one plane
B)
Prove theorem 32 with an Indirect Proof
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a.
Theorem 32
i.
If a line intersects a plane not containing it, then the
intersection contains only one point
1.
ii.
Hypothesis
1.
L intersects E in at least one point P, and
2.
E does not contain L
a.
Indirect Proof
3.
Supposition the intersection contains two points (Q
also)
a.
i.
Which one of our hypothesis get refuted b/c of
our drawing?
ii.
Therefore, our supposition is false proving that
theorem 32 is true
C)
Prove theorem 33 with an Indirect Proof
a.
Theorem 33
i.
Given a line and a point not on the line, there is exactly 1
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 Spring '09
 Johnson
 Logic, Algebra, Euclidean geometry, Mathematical terminology

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