No Clickers Bellwork State which postulate justifies each statement If D is in the interior of ABC, then mABD+ mDBC=mABC 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.
Bellwork Solution State which postulate justifies each statement If D is in the interior of ABC, then mABD+ mDBC=mABC Angle Addition Postulate
Bellwork Solution If M is between X and Y, then XM+MY=XY State which postulate justifies each statement If M is between X and Y, then XM+MY=XY Segment Addition Postulate
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
Use Postulates and Diagrams Section 2.4
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
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
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
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
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
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
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
Example Which of the following cannot be assumed from the diagram? r E Axis of symmetry Vertex
Homework 2.4 1-23, 30-34
Most Important Points Postulates 5-11 How to use postulates as a model Using postulates to show what’s true and what’s not