Bellwork

1. No Clickers Bellwork • State which postulate justifies each statement • If D is in the interior of ABC, then mABD+ mDBC=mABC • If M is between X and Y, then XM+MY=XY • Find the measure of MN if N is between M and P and MP=6x-2, MN=4x, and MP=16.

2. Bellwork Solution • State which postulate justifies each statement • If D is in the interior of ABC, then mABD+ mDBC=mABC Angle Addition Postulate

3. Bellwork Solution • State which postulate justifies each statement • If M is between X and Y, then XM+MY=XY Segment Addition Postulate

4. Bellwork Solution • Find the measure of MN if N is between M and P and MP=6x-2, MN=4x, and MP=16. P N M

5. Use Postulates and Diagrams Section 2.4

6. The Concept • Up until this point we’ve learned quite a few postulates and the basics of logic • Today we’re going to begin to put the two together

7. The Postulates • The postulates that we’re using can be found on pg. 96 • We’re going to briefly discuss them, however it is going to be up to you to find time to copy them out of the book and put them in your notes • The postulates we’ve seen • Postulate 1: Ruler Postulate • Postulate 2: Segment Addition Postulate • Postulate 3: Protractor Postulate • Postulate 4: Angle Addition Postulate Axis of symmetry Vertex

8. The Postulates • The postulates we’ve used, but never named • Postulate 5: Through any two points there exists exactly one line • Postulate 6: A line contains at least two points • Postulate 7: If two lines intersect, then their intersection is exactly one point • Postulate 8: Through any three non-collinear points there exists exactly one plane • Postulate 9: A plane contains at least three non-collinear points • Postulate 10: If two points lie in a plane, then the line containing them lies in the plane • Postulate 11: If two planes intersect, then their intersection is a line Axis of symmetry Vertex

9. Why do we need these? • When we see something occur we can now reference it by way of theory • For example • State the postulate illustrated in the pictures Axis of symmetry Vertex

10. Example • Another use is to use the postulates as a blueprint for statements about a diagram • For example • Use this diagram to write examples of Postulate 6 & 8 Postulate 6: If line l exists, then points R and S are on the line Postulate 8: If points W, R, S are non-collinear, then plane M exists

11. Perpendicular Figures • A line is a line perpendicular to a plane if and only if the line intersects the plane in a point and is perpendicular to every line in the plane that intersects it at the point • What? Axis of symmetry Vertex

12. Assumptions • When using postulates we have to be cognizant of the concern over assumed information • We can only use given information from a diagram • Assuming that properties based on “what looks good” is erroneous Axis of symmetry Vertex

13. Example • Which of the following cannot be assumed from the diagram? r E A C X B l s F Axis of symmetry Vertex

14. Homework • 2.4 • 1-23, 30-34

15. Most Important Points • Postulates 5-11 • How to use postulates as a model • Using postulates to show what’s true and what’s not