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8/25/2014Geometry1 Section 1.4 If-Then Statements and Postulates

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8/25/2014Geometry2 Objectives-What we’ll learn Recognize and analyze a conditional statement Write postulates about points, lines, and planes using conditional statements

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Postulate vs. Theorem A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven.

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8/25/2014Geometry4 Conditional Statement A conditional statement has two parts, a hypothesis and a conclusion. When conditional statements are written in if-then form, the part after the “if” is the hypothesis, and the part after the “then” is the conclusion. p → q represents “if p then q”

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8/25/2014Geometry5 Examples If you are 13 years old, then you are a teenager. Hypothesis: You are 13 years old Conclusion: You are a teenager

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8/25/2014Geometry6 Rewrite in the if-then form (Conditional Statement) All mammals breathe oxygen If an animal is a mammal, then it breathes oxygen. A number divisible by 9 is also divisible by 3 If a number is divisible by 9, then it is divisible by 3.

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8/25/2014Geometry7 Rewrite in the if-then form (Conditional Statement) Two lines intersect at a point. If two lines intersect, then they intersect at a point. Three non-collinear points determine a plane. If there are three non-collinear points, then they determine a plane.

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8/25/2014Geometry8 Writing a Counterexample Write a counterexample to show that the following conditional statement is false If x 2 = 16, then x = 4. As a counterexample, let x = -4. The hypothesis is true, but the conclusion is false. Therefore the conditional statement is false.

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8/25/2014Geometry9 Converse The converse of a conditional statement is formed by switching the hypothesis and the conclusion. The converse of p → q is q → p

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Rewrite in the Converse form. If you are 13 years old, then you are a teenager. If you are a teenager, then you are 13 years old. If a number divisible by 9, then it is also divisible by 3 If a number is divisible by 3, then it is divisible by 9.

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Rewrite in the Converse form. If two angles are vertical angles, then they are congruent. If two angles are congruent, then they are vertical angles. If a quadrilateral has 4 right angles, then it is a rectangle. If a quadrilateral is a rectangle, then it has 4 right angles.

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8/25/2014Geometry12 Point, Line, and Plane Postulates Postulate 1-1: Through any two points there exists exactly one line Postulate 1-2: Through any three noncollinear points there exists exactly one plane Postulate 1-3: A line contains at least two points Postulate 1-4: A plane contains at least three points not on the same line

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8/25/2014Geometry13 Postulate 2-5: If two points lie in a plane, then the line containing them lies in the plane Postulate 2-6: If two planes intersect, then their intersection is a line

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