Presentation on theme: "8/25/2014Geometry1 Section 1.4 If-Then Statements and Postulates."— Presentation transcript:
8/25/2014Geometry1 Section 1.4 If-Then Statements and Postulates
8/25/2014Geometry2 Objectives-What we’ll learn Recognize and analyze a conditional statement Write postulates about points, lines, and planes using conditional statements
Postulate vs. Theorem A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven.
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”
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
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.
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.
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.
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
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.
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.
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
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