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Postulates and Paragraph
Proofs
Eric Hoffman
Advanced Geometry
PLHS
Oct. 2007
Key Topics
• Postulate or Axiom: a statement that
describes a fundamental relationship
between basic terms in Geometry
– Ex. Through any two points there is exactly
one line
– Ex. The shortest distance between any two
points is a line
• These statements are always accepted
as true
Key Topics
• These are essential in writing proofs for
this chapter
Using Postulates
• Determine whether each statement is always,
sometimes, or never true using our knowledge
about postulates.
• If plane T contains EF and EF contains point G
then plane T contains point G
• For XY , if X lies in plane Q and Y lies in plane R
then, plane Q intersects plane R
• EF contains three non-collinear points
Key Topics
• Theorem: a statement or postulate that
has been shown to be true
• Once proven true, a theorem can be used
like a statement or postulate to justify that
other statements are true
Key Topics
• Proof: a logical argument in which each
statement you make is supported by a
statement that is accepted as true (can be a
axiom, postulate, theorem)
• Paragraph Proof: a type of proof in which you
write a paragraph to explain why a conjecture is
true for a given situation
All paragraph proofs
should start with what
is given and what we
want to prove
Proofs should end with a box which
denotes the end of your proof
Key Topics
• In the figure E is the midpoint of
AB and CD, and AB = CD.
Write a paragraph proof to
prove that AE  ED
Key Topics
• Given: E is the midpoint of AB and CD, and AB
= CD
• Prove: AE  ED
Proof:
Since E is the midpoint of AB by the Midpoint Theorem we know
that AE  EB, similarly we know that CE  ED. By the
definition of congruent segments we know that AE = EB = ½
AB, similarly we also know that CE = ED = ½ CD. Since we
know that AB = CD, by the multiplication property we can say
that ½ AB = ½ CD, and thus AE = ED. Therefore by the
definition of congruent segments AE ED □
Key Topics
• Homework pg. 91,92 10 – 30 even
11 problems!!