Presentation on theme: "Section 1.4 If-Then Statements and Postulates"— Presentation transcript:
1Section 1.4 If-Then Statements and Postulates 4/6/2017Geometry
2Objectives-What we’ll learn Recognize and analyze a conditional statementWrite postulates about points, lines, and planes using conditional statements4/6/2017Geometry
3Postulate vs. TheoremA postulate is a statement that is assumed true without proof.A theorem is a true statement that can be proven.
4Conditional 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”4/6/2017Geometry
5Examples If you are 13 years old, then you are a teenager. Hypothesis: Conclusion:You are a teenager4/6/2017Geometry
6Rewrite in the if-then form (Conditional Statement) All mammals breathe oxygenIf an animal is a mammal, then it breathes oxygen.A number divisible by 9 is also divisible by 3If a number is divisible by 9, then it is divisible by 3.4/6/2017Geometry
7Rewrite 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.4/6/2017Geometry
8Writing a Counterexample Write a counterexample to show that the following conditional statement is falseIf x2 = 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.4/6/2017Geometry
9ConverseThe converse of a conditional statement is formed by switching the hypothesis and the conclusion.The converse of p → q is q → p4/6/2017Geometry
10Rewrite 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 3If a number is divisible by 3, then it is divisible by 9.
11Rewrite 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.
12Point, Line, and Plane Postulates Postulate 1-1: Through any two points there exists exactly one linePostulate 1-2: Through any three noncollinear points there exists exactly one planePostulate 1-3: A line contains at least two pointsPostulate 1-4: A plane contains at least three points not on the same line4/6/2017Geometry
13Postulate 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 line4/6/2017Geometry