Deductive Reasoning

1
Deductive Reasoning

• The process of showing that certain statements
  follow logically from agreed-upon assumptions and
  proven facts is called deductive reasoning.
• In deductive reasoning you use a series of
  connected, orderly steps to show that a specific
  conclusion is true.
• Anyone familiar with the rules will be able to
  reach the same conclusion.

2
Deductive Reasoning

• You use deductive reasoning to solve an algebra
  problem  
• Solve the equation for x. Give a reason for each
  step in the process.  
• Solution     
• 3(2x 1) 2(2x 1) 7 42 5x  The
  original equation.   
• 5(2x 1) 7 42 5x  Combining like
  terms.   
•   5(2x 1) 35 5x  Subtraction property of
  equality.   
•   10x 5 35 5x  Distributive property.   
•    10x 30 5x Subtraction property of
  equality.   
•    15x 30 Addition property of equality.   
•    x 2 Division property of equality. 

3
Deductive Reasoning

• A conjecture that is proven using deductive
  reasoning is called a theorem
• The proof of a conjecture using established facts
  can be presented in a variety of formats
• A paragraph proof is a logical series of
  statements that show a theorem is true
• A flow chart proof is a diagram listing each step
  and its supporting reason
• A two column proof lists a series of steps in the
  left column and reasons in the right column

4
Deductive Reasoning

• In each diagram, ray AC bisects obtuse angle BAD
• Make a conjecture about the angles created
• Conjecture If an obtuse angle is bisected,
• then the two newly formed congruent angles are
  _________

5
Deductive Reasoning

• A paragraph proof of this conjecture is in your
  book on page 101.
• A two column proof would break down the paragraph
  proof into a list of statements and reasons.
• A flow chart proof would draw a box for each
  statement, list the reason below the box, and
  draw an arrow leading from one box to the next.

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Deductive Reasoning

• Do the Investigation on page 102 Overlapping
  Segments
• Measure segments AC and BD and propose a
  conclusion for the conjecture
• Use deductive reasoning to prove the conjecture