BIG IDEA: Reasoning and Proof ESSENTIAL UNDERSTANDINGS: Logical reasoning from one step to another is essential in building a proof. Logical reasoning.

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Presentation transcript:

BIG IDEA: Reasoning and Proof ESSENTIAL UNDERSTANDINGS: Logical reasoning from one step to another is essential in building a proof. Logical reasoning from one step to another is essential in building a proof. Reasons in a proof include given information, definitions, properties, postulates, and previously proven theorems. Reasons in a proof include given information, definitions, properties, postulates, and previously proven theorems. MATHEMATICAL PRACTICE: Construct viable arguments and critique the reasoning of others

  Follow the steps of the brainteaser using your age. Then try it using a family member’s age. What do you notice? Explain how the brainteaser works.  Write down your age.  Multiply it by 10.  Add 8 to the product.  Double that answer and then subtract 16.  Finally, divide the result by 2. GETTING READY

  Let be real numbers.  Addition Property:  Subtraction Property:  Multiplication Property:  Division Property:  Reflexive Property:  Symmetric Property:  Transitive Property:  Substitution Property:  Distributive Property: Algebraic Properties of Equality

  a) EX 1: What is the value of x? Justify each step.

  b) EX 1: What is the value of x? Justify each step.

  The properties of equality reviewed in the beginning of this lesson add to the students’ “toolbox” for writing proofs using deductive reasoning. It is important to make a connection between the algebraic proofs that you unknowingly completed throughout all of Algebra and the proofs that you will complete in Geometry. You should understand that the process of solving an equation is an algebraic proof, although the justifications for each step are not generally written down. Therefore, proofs are not unique to Geometry. Math Background

  Reflexive Property:  Symmetric Property:  Transitive Property:  Properties of equality are true for any numbers, while congruence properties are true for geometric figures Properties of Congruence

  a) Example 2 StatementsReasons 1.1.Given Segment Addition Postulate 5. 6.

  b) A baseball diamond is shown below. The pitcher’s mound is at. Use the information to find the. Example 2

  Proof: a convincing __________________ that uses ____________________ reasoning. A proof __________________ shows why a conjecture is __________  Two-column proof: lists each __________________ on the __________and the justification or ____________ for each statement is on the __________. Each statement must follow ______________________ from the __________ before it. Proofs

  Given:  Prove: Writing a Two-Column Proof StatementsReasons 1.1. Given Addition Property of Equality 4. 5.

  Given:  Prove: Writing a Two-Column Proof StatementsReasons 1.1.Given 2. 3.

 2.4 p – 14 all, 16 – 28 evens, 29 – 32 all, 36 – 45x3 20 questions