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A Perfect Proof

A Perfect Proof. By Mrs. Lee Huang. A perfect proof must always include the following components (yes, all of them!): A “given” statement – this is your starting point; the fact(s) that you start working with A “prove” statement – this is the goal you want to reach/prove

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A Perfect Proof

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  1. A Perfect Proof By Mrs. Lee Huang

  2. A perfect proof must always include the following components (yes, all of them!): • A “given” statement – this is your starting point; the fact(s) that you start working with • A “prove” statement – this is the goal you want to reach/prove • A picture – a visual that helps you understand the relationship of figures • A statement & reason, or sTr, chart – the step-by-step logical process that connects the “given” statement to the “prove” statement The Players

  3. Statement The sTrChart • Statements must be numbered. • The first statement is usually the given statement. • The statements are written in “math form” – equations, congruencies, etc. • The statement should match the conclusion of the corresponding reason. Reason Reasons must be numbered to match their corresponding statements The reason for the given statement is always “given.” All other reasons must be accepted definitions, theorems or postulates written out fully. The condition/hypothesis, “if” statement, must be met either through previous step(s) or visually in the figure.

  4. B ● ● C ● ● D A 1 2 3 So what does a good proof look like? ● O

  5. Show me the logic! B ● ● C ● ● D A 1 2 3 ● O

  6. Show me the logic! B ● ● C ● ● D A 1 2 3 ● O

  7. Show me the logic! B ● ● C ● ● D A 1 2 3 ● O

  8. Show me the logic! B ● ● C ● ● D A 1 2 3 ● O b = c b = a = d c 3. Transitive Property = d a

  9. Show me the logic! B ● ● C ● ● D A 1 2 3 ● O 4. Reflexive Property

  10. Show me the logic! B ● ● C ● ● D A 1 2 3 ● O a = b c = d a – c = b –d 5. Subtraction Property

  11. Draw the “given” into the figure! It’ll help you visualize the information. Recap it! B ● ● C ● ● D A 1 2 3 Write the “prove” statement at the bottom. It can help you to focus on your next steps. ● O

  12. The hypothesis, “if” phrase, of each reason should be met either through the figure or an earlier statement. Recap it! B ● ● C ● ● D A 1 2 3 Also, the conclusion, “then” phrase, of each reason should match the structure of its corres-ponding statement. ● O

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