Name vertical angles and linear pairs. Name a pair of complementary angles and a pair of supplementary angles.

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Presentation transcript:

Name vertical angles and linear pairs. Name a pair of complementary angles and a pair of supplementary angles.

Geometry: Chapter 2 2.5: If-Then Statements and Deductive Reasoning Obj: Identify hypothesis and conclusions of if- then statements. Use laws of logics to make logical statements

If-then statement: Sentence with an if-then situation Hypothesis: (p) the “if” part of a conditional Conclusion: (q) the “then” part of a conditional – Example: An if-then statement is given below. Identify the hyp. and conclusion. If I study for the test, then I will receive a higher grade.

In the if-then statement, circle the hypothesis and underline the conclusion 1) If I do my homework then I will learn the material. 2) I will go to the game if my parents give me money. 3) If a car is a Corvette, then it is a Chevrolet

Rewrite the statement as an if-then statement. 4) All students love geometry. 5) An equilateral triangle is a triangle with 3 congruent sides.

Deductive Reasoning Deductive Reasoning: Uses, __________, ________________, ________________, and ____________ to make a logical argument. facts definitionsAccepted properties Laws of logic

Laws of Logic Law of Detachment: if the hypothesis of an if- then statement is true, then the conclusion must be true. Logic Notation: If p, then q P Therefore q.

Example If it rains, then the grass will be wet. It is raining outside. Therefore, _______________________ * Only goes one way, can not have the conclusion, and therefore hypothesis.

Law of Syllogism (Logic Chain) If p implies q and q implies r are true statements, then p implies r is true. Logic Notation: If p then q If q then r Therefore, if p then r

Example If I forget my homework, then I will receive a zero. If I receive a zero my grade will go down. If my grade goes down, then my parents will get mad

– If a car is a corvette, then it is a chevy. – Ms. Thelen owns a corvette.

What can you conclude based on the law of syllogism? If I drive to school, then I will pick up Bob. If I pick up Bob, then he will pay me $5.