Chapter 2.3 Notes: Apply Deductive Reasoning

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Chapter 2.3 Notes Apply Deductive Reasoning

• Goal You will use deductive reasoning to form a
  logical argument.

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• Deductive reasoning uses facts, definitions,
  accepted properties, and the laws of logic to
  form a logical argument.
• This is different from inductive reasoning, which
  uses specific examples and patterns to form a
  conjecture.

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• Laws of Logic
• Law of Detachment
• If the hypothesis of a true conditional
  statement is true, then the conclusion is also
  true.
• Ex.1 Use the Law of Detachment to make a valid
  conclusion in the true situation.
• a. If two segments have the same length, then
  they are congruent. You know that BC XY.
• b. Mary goes to the movies every Friday and
  Saturday night. Today is Friday.

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• Law of Syllogism
• If p, then q.
• If q, then r.
• If p, then r.
• Ex.2 If possible, use the Law of Syllogism to
  write a new conditional statement that follows
  from the pair of true statements.
• a. If Rick takes chemistry this year, then Jesse
  will be Ricks lab partner.
• If Jesse is Ricks lab partner, then Rick
  will get an
• A in chemistry.

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• b. If x2 gt 25, then x2 gt 20.
• If x gt 5, then x2 gt 25.
• c. If a polygon is regular, then all angles in
  the interior of the polygon are congruent.
• If a polygon is regular, then all of its
  sides are congruent.

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• Ex.3 Use the Law of Detachment to make a valid
  conclusion in the true situation.
• a. If two angles are right angles, then they are
  congruent. Angle C and Angle D are right angles.
• b. If Nathan is enrolled at Metro High School,
  then Nathan has an ID number. Nathan is enrolled
  at Metro High School.

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• Ex.4 If possible, use the Law of Syllogism to
  write a new conditional statement that follows
  from the pair of true statements.
• a. If the radius of a circle is 4 ft, then the
  diameter is 8 ft. If the radius of a circle is 4
  ft, then its area is 16p ft2.
• b. If Joe takes Geometry this year, then he will
  take Algebra 2 next year. If Joe takes Algebra 2
  next year, then he will graduate.
• c. If y3 8, then y 2. If y 2, then 3y 4
  10.

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• Ex.5 If 90o lt lt 180o, then is
  obtuse. The measure of is 155o. Using the
  Law of Detachment, what statement can you make?
• Ex.6 If Jenelle gets a job, then she can afford
  a car. If Jenelle can afford a car, then she will
  drive to school. Using the Law of Syllogism, what
  statement can you make?