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Simple Proofs & Theorems 1 and 2 Geometry 1.4

Simple Proofs & Theorems 1 and 2 Geometry 1.4. Definition : Postulates are statements that are assumed true. They are not proved to be true. Definition : Theorems are statements that are proved true using postulates and/or theorems that have already been proved .

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Simple Proofs & Theorems 1 and 2 Geometry 1.4

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  1. Simple Proofs & Theorems 1 and 2 Geometry 1.4

  2. Definition: Postulates are statements that are assumed true. They are not proved to be true. Definition: Theorems are statements that are proved true using postulates and/or theorems that have already been proved. Two Types of Statements:Postulates & Theorems

  3. Theorem 1: If two angles are right angles, then they are congruent. Theorem 2: If two angles are straight angles, then they are congruent.

  4. Theorem 1: If two angles are right angles, then they are congruent. How to prove a theorem: 1. Rewrite the “IF – THEN” statement as “Given” and “Prove” 2. Draw a diagram with labels for all referenced objects 3. Write a “Two-Column” Proof

  5. Theorem 2: If two angles are straight angles, then they are congruent. How to prove a theorem: 1. Rewrite the “IF – THEN” statement as “Given” and “Prove” 2. Draw a diagram with labels for all referenced objects 3. Write a “Two-Column” Proof

  6. Example of (Very) Simple Two Column Proof: Given: <A and <B are right angles Prove: 1. 2.

  7. Example of (Very) Simple Two Column Proof: Given: m<BAC=30 and m<DAC=30 Prove: 1. 2.

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