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Lesson 2.3 Notes DEDUCTIVE REASONING

Lesson 2.3 Notes DEDUCTIVE REASONING. Mrs. Reese Geometry CP. Deductive Reasoning. Deductive reasoning is the process of using facts, rules, definitions, and properties to reach a valid conclusion.

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Lesson 2.3 Notes DEDUCTIVE REASONING

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  1. Lesson 2.3 NotesDEDUCTIVE REASONING Mrs. ReeseGeometry CP

  2. Deductive Reasoning • Deductive reasoning is the process of using facts, rules, definitions, and propertiesto reach a valid conclusion. • Different from inductive reasoning which uses observations and examples to form conjectures.

  3. Deductive Reasoning • In this lesson we use 2 Laws of Logic to make valid conclusions. • The Law of Detachment and • The Law of Syllogism

  4. Law of Detachment • If you have a true conditional statement… • If a student likes school, then he/she will get good grades. • and there is a specific case where the hypothesis is true… • Erica(a student) likes school. • then the conclusion must also be true! • Erica will get good grades.

  5. Law of Detachment (example 2) • If 2 angles are vertical, then they are congruent. • <1 and <2 are vertical angles. • Therefore… • <1 and <2 are congruent.

  6. Law of Detachment (example 3) • If a person likes to run, then he/she likes to exercise. • John likes to run. • Therefore… • John likes to exercise.

  7. Law of Syllogism This is called a Logical Chain • If you have a series of 2 or more logically linked true conditional statements… • If a student packs up before Mrs. Reese tells him, then he will be the last out of class. • If a student is last out of class, then he will be late to his next class. • If a student is late to class, then he will get detention. • You can write another true conditional statement as the conclusion, by combining the first hypothesis (if) and the last conclusion (then). • Therefore…If a student packs up before Mrs. Reese tells him, then he will get detention.

  8. Law of Syllogism (example 2)

  9. Law of Syllogism (example 3) If 2 angles are vertical, then they are congruent. If 2 angles are congruent, then they have the same measure. Therefore… If 2 angles are vertical, then they have the same measure.

  10. Invalid Conclusions If a student is sick, then he is absent. Jason is absent. Therefore…Jason is sick. INVALID example of the Law of Detachment because the second statement is based on the conclusion instead of the hypothesis of the original conditional statement.

  11. Invalid Conclusions If an animal is a bird, then it can fly. If an animal can fly, then it has wings. Therefore…If an animal has wings, then it is a bird. INVALID example of the Law of Syllogism because the third statement does not start with the first hypothesis.

  12. Classwork Lesson 2.3 Practice

  13. Lesson 2.3 Practice 1. If a person is in Mrs. Reese’s 5th period class, then the person is taking geometry. Timmy is in Mrs. Reese’s 5th period class. Therefore… Timmy is taking Geometry.

  14. Lesson 2.3 Practice 2. If a person scores 85-92 on a geometry test, then the person receives a B on the test. Meagan scored 87 on the last geometry test.. Therefore… Meagan received a B on the test.

  15. Lesson 2.3 Practice 3. If you finish your chores on time, you may use the car tonight. You finish your chores on time. Therefore... You may use the car tonight.

  16. Lesson 2.3 Practice 4. If I go shopping, I will buy a new umbrella. If it rains on Saturday, then I am going shopping. If I buy a new umbrella, then I won’t get wet. Therefore… If it rains on Saturday, then I won’t get wet.

  17. Lesson 2.3 Practice 5. If it is warm, then it is spring. If flowers are blooming, then it is warm. If you see bees, then flowers are blooming. Therefore… If you see bees, then it is spring.

  18. Lesson 2.3 Practice 6. If school is canceled, then Shelbie will stay home all day. If it snows too much in Council Bluffs, then school is canceled. If Shelbie stays home all day, then she will go on the internet. Therefore… If it snows too much in Council Bluffs, then Shelbie will go on the internet.

  19. Assignment Complete the back side of this worksheet. Look in magazines or sale papers and find examples of conditional statements. Bring in at least one example by Monday, October 11th.

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