1. Chapter 3 Parallel and Perpendicular Lines
3.1 Identify Pairs of Lines and Angles

2. New in this Section:
So far we have looked at angle pairs formed by 2 lines
Vertical angles
Supplemental angles
Complementary angles
Now we will look at angle pairs formed by 3 lines
Interior angles
Same side (consecutive)
Alternate interior
Exterior angles
Corresponding angles

3. Euclidean Geometry
High School Geometry, invented by a Greek mathematician Euclid is based on 5 principals known as postulates
We know them they are easy
A line can be drawn between 2 points
Any line segment can be a line
Circles exist with a given radius
All right angles are congruent
Parallel lines exist
In this section we will study the 5th postulate, presented in our book as postulate 13

4. The world of Geometry
Everything in geometry that we do in high school is proven based on the idea that these 5 postulates are fact
1-4 are easy to prove
5 is not, in fact it has never been proven!
This is why many forms of geometry exist!
Global Geometry!
Why is Euclid’s Geometry so popular?

5. Every line that does not intersect is either Parallel or Skew!
Skew lines do not intersect but do not exist in the same plane
Think of a cube, the top of the front face and the bottom of the rear face
Parallel lines are lines that do not intersect and exist in the same plane

6. Pair up and discuss
How many pairs of parallel sides? How many pairs of perpendicular sides?

7. Transversal Any line that intersects two other linesm
Discussion: which line is the transversal?

8. Postulate 13(Euclid’s 5th)
If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line
Ex. There is exactly one line through P parallel to line L.
Line parallel To line L P
Any other line is not parallel L

9. Perpendicular Postulate
Same idea as parallel postulate
If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line
Ex. There is exactly one line through P perpendicular to line L.
Line Perpendicular To line L P
Any other line is not perpendicular L

10. Symbolic Representations
AB || CD
Translation: line AB is parallel to line CD n
Two arrow heads are the symbol here m L
Translation line n is parallel to line m

11. Symbolic Representations
AB ┴ CD
Translation: line AB is perpendicular to line CD m
The square is the symbol here n
Translation: line n is perpendicular to line m

12. Homework
P. 150
1-10, 24-28, 34-37