Geometry Chapter 2 2 3 APPLY DEDUCTIVE REASONING

Geometry Chapter 2 2 -3: APPLY DEDUCTIVE REASONING

Warm-up Any Definition can be written as a Biconditional Statement. For Warm-up: Write some of our past vocabulary terms as Biconditional statements. Terms: Collinear Points Supplementary Angles Congruent Segments Complementary Angles Congruent Angles

2 -3: Apply Deductive Reasoning Objective: Students will be able to deductive reasoning to form a logical argument in order to reach a logical conclusion Agenda Ø Deductive Reasoning ØLaw of Detachment ØLaw of Syllogism ØInductive/Deductive Reasoning

Deductive Reasoning • Deductive Reasoning uses postulates, definitions, accepted properties, and the laws of logic to form a logical argument. • Laws of Logic • Law of Detachment • If the hypothesis of a true conditional statement is true, then the conclusion is also true.

Laws of Logic – Law of Detachment Then Mary will go to the movies tonight.

Deductive Reasoning • Deductive Reasoning uses postulates, definitions, accepted properties, and the laws of logic to form a logical argument. • Laws of Logic • Law of Syllogism • If hypothesis a, then conclusion b • If hypothesis b, then conclusion c • If hypothesis a, then conclusion c To sum it up, event a leads into event b, which then leads into event c. So overall, event a ultimately leads into event c.

Laws of Logic – Law of Syllogism • Examples: Use the Law of Syllogisms 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 Rick’s lab partner. If Jesse is Rick’s lab partner, then Rick will get an A in Chemistry. Solution: If Rick takes Chemistry this year, then Rick will get an A in Chemistry

Laws of Logic – Law of Syllogism

Laws of Logic – Law of Syllogism • Examples: If possible, use the Law of Syllogisms to write a new conditional statement that follows from the pair of true statements. 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. Solution: A new statement cannot be made; Neither statement has a conclusion that is the other statement’s hypothesis.

Deductive and Inductive Reasoning • In Geometry, you will frequently use inductive reasoning to make conjectures by analyzing Patterns. • You will also use deductive reasoning to show whether these statements are true or false through the use of logical arguments. • You will need to be able to tell which type of reasoning is being used at any given time.

Deductive and Inductive Reasoning Conjecture: An even integer multiplied by any other integer always results in an even integer.

Deductive and Inductive Reasoning Final (Proven) Result: The product of an even integer and any other integer is always an even integer.

Deductive and Inductive Reasoning • Example: Decide whether inductive or deductive reasoning is used to reach the conclusion. Explain your reasoning. a. ) Each time Monica kicks a ball up in the air, it returns to the ground. So the next time Monica kicks a ball up in the air, it will return to the ground. Inductive Reasoning: A pattern is used to arrive at a conclusion b. ) All reptiles are cold-blooded. Parrots are not cold blooded. Sue’s pet parrot is not a reptile. Deductive Reasoning: Facts about animals and the laws of logic are used to reach a conclusion

Deductive and Inductive Reasoning • Example: Decide whether inductive or deductive reasoning is used to reach the conclusion. Explain your reasoning. c. ) Whenever it rains in the morning, afternoon baseball games are canceled. The baseball game this afternoon was not canceled. So, it did not rain this morning. Deductive Reasoning: The laws of logic are used to reach a conclusion d. ) Every time Tom has eaten strawberries, he has had a mild allergic reaction. The next time he eats strawberries, Tom will have a mild allergic reaction. Inductive Reasoning: The conclusion is based off a pattern of past occurrences.

HW 2 -3 Pgs. 82 #’s 1 -10, 16 -19, 21, 22, 25 -38 (EC) – 11