2'5 Postulates

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2.5 Postulates Paragraph Proofs
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2 Types of Rules to Follow in Geom

• Postulate (post) or axiom statements that we
  all agree are true

Theorems (thm) statements that must be proved
using facts, alg props, posts, previously proved
thms, defs
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• Post 2.1 Thru any 2 pts, theres exactly
  _________.
• Post 2.2 Thru any 3 pts not on same line,
  theres exactly _________.
• Post 2.3 A line contains _________.
• Post 2.4 A plane contains ______________________
  _____.

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• Post 2.5 If 2 pts lie in same plane ? line
  containing those pts __________________.
• Post 2.6 If 2 lines intersect ? they intersect
  in _________.
• Post 2.7 If 2 planes intersect ? they intersect
  in _________.

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Examples A, S or N true. Explain.

• If pts A, B, C are in plane M ? theyre
  collinear.
• Theres exactly 1 plane with pts P, Q, R.
• Theres at least 2 lines thru pts M N.

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Note
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Proof logical argument to prove statements

• Paragraph Proof proof in form of paragraph in
  which you list ___________________________________
  ___________________ to justify each step
• 5 Essential Parts of a Proof
• 1. 4.
• 2. 5.
• 3.

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Example Write a paragraph proof

• Given that M is the midpt of PQ, write a
  paragraph proof to show that PM MQ.
• Given
• Prove

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Midpt Thm If M is midpt of AB ? AM MB.
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Assignment

• 2.5 p. 92 (12-30 even, 34, 40-48 even)