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.

No Clickers

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

• 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.

MN

P

3

186

1626

x

x

x

12

12)3(4

4

MN

MNx

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

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

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

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?

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

Example• Which of the following cannot be assumed from the

diagram?

AB

C X

sF

E

r

l

, ,A B C arecollinear

EF �������������� �

BC plane r�������������� �

intersectsEF ABat B���������������������������������������� ���

line AB�������������� �

, ,B C X arecollinear

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