Aim: What are postulates

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Aim What are postulates?

• Do Now Complete Statement/Reason Handout

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A postulate, or axiom, is a statement that is
accepted as true without proof. A theorem is a
statement that is proved by deductive reasoning.
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The First Postulates Used in Proving Statements

• The Reflexive Property of Equality a a
• Postulate 3.1 A quantity is equal to itself.
• For example
• 1. The length of a segment is equal to itself.
• CD CD
• DE DE
• EC EC
  
• 2. The measure of an angle is equal to itself.

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The First Postulates Used in Proving Statements

• The Symmetric Property of Equality If a b,
  then b a.
• Postulate 3.2 An equality may be expressed in
  either order.
• For example
• 1. If LM NP, then NP LM.
• 2. If , then
  .

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The First Postulates Used in Proving Statements

• The Transitive Property of Equality
• If a b and b c, then a c.
• Postulate 3.3 Quantities equal to the same
  quantity are equal to each other.
• For example
• 1. If and , then
  .