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3-5 Justifying Conclusions

3-5 Justifying Conclusions. The basis of mathematical reasoning is the making of conclusions justified by definitions, postulates, or theorems. 3-5 Justifying Conclusions.

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3-5 Justifying Conclusions

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  1. 3-5 Justifying Conclusions • The basis of mathematical reasoning is the making of conclusions justified by definitions, postulates, or theorems.

  2. 3-5 Justifying Conclusions • A proof of a conditional is a sequence of justified conclusions starting with the antecedent and ending with the consequent.

  3. 3-5 Justifying Conclusions Example of Mathematical Proof Given: 5x + 16 = 46 Prove: x = 6 Conclusions | Justifications 1. 5x + 16 = 46 | 1. Given 2. 5x = 30 | 2. Addition Prop of = 3. x = 6 | 3. Mult. Prop of =

  4. 3-5 Justifying Conclusions Example of Geometric Proof Given: P and Q are points on –O Prove: OP = OQ Conclusions | Justifications 1. P and Q are points on –O | 1. Given 2. OP = OQ | 2. Def. of Circle

  5. 3-5 Justifying Conclusions Example of Structure of Proof Given: Where you start your proof Prove: Where you end up Conclusions | Justifications 1. Where you start | 1. Given 2. Intermediate Step(s) | 2. Reason(s) 3. Intermediate Step(s) | 3. Reason(s) 4. Where you end up | 4. Reason Justifications can be GIVENS, DEFINITIONS, POSTULATES, THEOREMS, THINGS ALEADY PROVEN IN THE PROOF.

  6. 3-5 Justifying Conclusions 1 2 Given: Figure at right Prove: mÐ1 + mÐ2 = 180 Conclusions | Justifications 1. Ð1 and Ð2 form a | linear pair | 1. 2. Ð1 and Ð2 are | supplementary Ð’s | 2. 3. mÐ1 + mÐ2 = 180 | 3. n

  7. 3-5 Justifying Conclusions Given: X and Y are points on –Z Prove: XZ = YZ Conclusions | Justifications 1. | 1. 2. | 2.

  8. 3-5 Justifying Conclusions Given: mÐ1 + mÐ2 = 90; mÐ2 + mÐ3 = 90 Prove: mÐ1 = mÐ3 Conclusions | Justifications 1. | 1. 2. | 2. 3. | 3. 2 1 3

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