1. 2.3 Postulates and Diagrams
Geometry

2. Geometry 2.3 Postulates and Diagrams
Goals
Recognize and analyze conditional statements.
Know and use related statements.
May 15, 2018
Geometry 2.3 Postulates and Diagrams

3. Geometry 2.3 Postulates and Diagrams
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
May 15, 2018
Geometry 2.3 Postulates and Diagrams

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

5. Geometry 2.3 Postulates and Diagrams
2.1 Two Point Postulate
Through any two points there exists exactly one line.
May 15, 2018
Geometry 2.3 Postulates and Diagrams

6. Geometry 2.3 Postulates and Diagrams
2.2 Line-Point Postulate
A line contains at least two points.
May 15, 2018
Geometry 2.3 Postulates and Diagrams

7. 2.3 Line Intersection Postulate
If two lines intersect, then their intersection is exactly one point.
May 15, 2018
Geometry 2.3 Postulates and Diagrams

8. Geometry 2.3 Postulates and Diagrams
2.4 Three Line Postulate
Through any three noncollinear points there exists exactly one plane.
May 15, 2018
Geometry 2.3 Postulates and Diagrams

9. Geometry 2.3 Postulates and Diagrams
Where do we use this?
May 15, 2018
Geometry 2.3 Postulates and Diagrams

10. 2.5 Plane-Point Postulate
A plane contains at least three noncollinear points.
May 15, 2018
Geometry 2.3 Postulates and Diagrams

11. Geometry 2.3 Postulates and Diagrams
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
May 15, 2018
Geometry 2.3 Postulates and Diagrams

12. 2.7 Plane Intersection Postulate
If two planes intersect, then their intersection is a line.
May 15, 2018
Geometry 2.3 Postulates and Diagrams

13. Geometry 2.3 Postulates and Diagrams
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.
May 15, 2018
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.
May 15, 2018
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.
May 15, 2018
Geometry 2.3 Postulates and Diagrams

16. Geometry 2.3 Postulates and Diagrams
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 .
May 15, 2018
Geometry 2.3 Postulates and Diagrams