Postulate 1-1 Through any two points, there is exactly one line. Can you imagine making more than one unique line (as defined in this class) that passes through the same two points?

Postulate 1-2 If two unique lines intersect, then they intersect in exactly one point. Try to draw an example of this in your notes. Can you think of this postulate ever not being true when you use the geometric definition of a line?

Postulate 1-3 If two distinct planes intersect, then they intersect in exactly one line. Imagine your desktop and notebook are each planes. If you hold the edge of your notebook against the surface of the desk, the two meet at the notebook’s edge. In what ways does this do a good or poor job of modeling the postulate?

Postulate 1-4 Through any three noncollinear points there is exactly one plane. What does collinear mean? What does noncollinear mean? Can you use this postulate to deduce the meaning of the words?

Postulate 1-5 Postulate 1 – Ruler Postulate The points on a line can be paired with real numbers in such a way that any two points can have coordinates 0 and 1. This means that I can choose two points on a line, label them 0 and 1, like on a ruler. Once a coordinate system has been chosen in this way, the distance between any two points equal the absolute value of the difference of their coordinates. This means that once we establish the distance from 0 to 1 and therefore 1 to 2, 2 to 3 and so on, we have created a ruler we can use to measure length In other words: “rulers work with segments”

Postulate 1-6 Segment addition postulate: If three points, A, B and C are collinear, and B is between A and C, then AB+BC=AC

The protractor postulate Just like the ruler postulate, the protractor postulate says that angles can be measured with a protractor.

Postulate 1-8 angle addition postulate If point B is in the interior of  AOC, then m  AOB+ m  BOC=m  AOC O AB C

Distance formula The Horizontal distance between the two points = a in the Pythagorean theorem. The vertical distance between the two points =b in the Pythagorean theorem. So, Y 2 -Y 1 = B X 2 -X 1 = A A B D

Midpoint Formula Similarly, we can find the midpoint of d by finding the halfway point of a and b. a b L M N d

3-1 Same side interior angles are supplementary (and its converse)

Corresponding Angles are congruent (and its converse)

Alternate exterior angles are congruent (and its converse)

How is this related to the transitive prop??

Which previous theorems does this combine?

What is this the converse of?