Geometry

1. Geometry 2.3 Postulates and Diagrams

2. Goals • Recognize and analyze conditional statements. • Know and use related statements. Geometry 2.3 Postulates and Diagrams

3. Using Postulates • Postulate: a statement assumed to be true without proof. • We’ve studied four postulates: • Ruler Postulate • Segment Addition Postulate • Protractor Postulate • Angle Addition Postulate Geometry 2.3 Postulates and Diagrams

4. Point, Line, and Plane Postulates Page 84 Refer to the Postulates as needed

5. 2.1 Two Point Postulate Through any two points there exists exactly one line. Geometry 2.3 Postulates and Diagrams

6. 2.2 Line-Point Postulate A line contains at least two points. Geometry 2.3 Postulates and Diagrams

7. 2.3 Line Intersection Postulate If two lines intersect, then their intersection is exactly one point. Geometry 2.3 Postulates and Diagrams

8. 2.4 Three Line Postulate Through any three noncollinear points there exists exactly one plane. Geometry 2.3 Postulates and Diagrams

9. Where do we use this? Geometry 2.3 Postulates and Diagrams

10. 2.5 Plane-Point Postulate A plane contains at least three noncollinear points. Geometry 2.3 Postulates and Diagrams

11. 2.6 Plane Line Postulate If two points lie in a plane, then the line containing them lies in the plane. a.k.a Flat Plane Postulate Geometry 2.3 Postulates and Diagrams

12. 2.7 Plane Intersection Postulate If two planes intersect, then their intersection is a line. Geometry 2.3 Postulates and Diagrams

13. Rewriting Postulates Rewrite postulate 2.1 in if-then form. Post. 2.1: Through any two points there exists exactly one line. Possible Answer: If there are two points, then there is exactly one line that passes through them. Geometry 2.3 Postulates and Diagrams

14. Try it. Rewrite in if-then form: A line contains at least two points. Possible solution: If a figure is a line, then it contains at least two points. Geometry 2.3 Postulates and Diagrams

15. If a figure is a line, then it contains at least two points. Which are true? • Write the converse, inverse and contrapositive. • Converse: If a figure contains at least two points, then it is a line. • Inverse: If a figure is not a line, then it doesn’t contain at least two points. • Contra: If a figure doesn’t contain at least two points, then it is not a line. Geometry 2.3 Postulates and Diagrams

16. Why postulates? They are essential building blocks for making proofs. You don’t need to memorize them word for word, but you do need to memorize what they are and what they mean. We now have seen 11 out of the 18 we will use this year. They are listed in the book A105 . Geometry 2.3 Postulates and Diagrams