Geometry CH 1-7 Patterns & Inductive Reasoning Using deductive reasoning. Objective.

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Geometry CH 1-7 Patterns & Inductive Reasoning Using deductive reasoning. Objective

Geometry CH 1-7 Patterns & Inductive Reasoning deductive reasoning Vocabulary

Geometry CH 1-7 Patterns & Inductive Reasoning Deductive reasoning is the process of using logic to draw conclusions from given facts, definitions, and properties.

Geometry CH 1-7 Patterns & Inductive Reasoning Is the conclusion a result of inductive or deductive reasoning? Example 1A: Media Application There is a myth that you can balance an egg on its end only on the spring equinox. A person was able to balance an egg on July 8, September 21, and December 19. Therefore this myth is false. Since the conclusion is based on a pattern of observations, it is a result of inductive reasoning.

Geometry CH 1-7 Patterns & Inductive Reasoning Is the conclusion a result of inductive or deductive reasoning? Example 1B: Media Application There is a myth that the Great Wall of China is the only man-made object visible from the Moon. The Great Wall is barely visible in photographs taken from 180 miles above Earth. The Moon is about 237,000 miles from Earth. Therefore, the myth cannot be true. The conclusion is based on logical reasoning from scientific research. It is a result of deductive reasoning.

Geometry CH 1-7 Patterns & Inductive Reasoning Check It Out! Example 1 There is a myth that an eelskin wallet will demagnetize credit cards because the skin of the electric eels used to make the wallet holds an electric charge. However, eelskin products are not made from electric eels. Therefore, the myth cannot be true. Is this conclusion a result of inductive or deductive reasoning? The conclusion is based on logical reasoning from scientific research. It is a result of deductive reasoning.

Geometry CH 1-7 Patterns & Inductive Reasoning Syllogism Some problems require students to use the law of detachment (If p→q is a true statement and p is true, then q is true) and the law of syllogism (If p→q and q→r are true statements, then p→r is a true statement) to draw conclusions from given statements.

Geometry CH 1-7 Patterns & Inductive Reasoning Another valid form of deductive reasoning is the Transitive Property (or Law of Syllogism). It allows you to draw conclusions from two conditional statements when the conclusion of one is the hypothesis of the other. Law of Syllogism (Transitive relation) If p  q and q  r are true statements, then p  r is a true statement.

Geometry CH 1-7 Patterns & Inductive Reasoning Properties of Equality and Real Numbers Addition Property: Subtraction Property: Multiplication Property: Division Property: Substitution Property: Distributive Property:

Geometry CH 1-7 Patterns & Inductive Reasoning Properties of Congruence Reflexive Property: Symmetric Property: Transitive Property:

Geometry CH 1-7 Patterns & Inductive Reasoning Determine if each conjecture is valid? 2. Given: If n is a natural number, then n is an integer. If n is an integer, then n is a rational number is a rational number. Conjecture: is a natural number. not valid Lesson Quiz: Part II 3. Given: If an American citizen is at least 18 years old, then he or she is eligible to vote. Anna is a 20-year-old American citizen. Conjecture: Anna is eligible to vote. valid

Geometry CH 1-7 Patterns & Inductive Reasoning Homework: Page-50 Problems 1-10