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

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

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

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?

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

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

Transversal Any line that intersects two other lines m Discussion: which line is the transversal?

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

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

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

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

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