CHAPTER THREE OBJECTIVES:
Chapter three is a quick chapter but does pack a punch. You will make conjectures about lines and angles and determine the validity of the conjectures. You will use the information that you learned in algebra about slopes of equations of lines to investigate geometric relationships including parallel and perpendicular lines. You will construct a set of parallel and perpendicular lines. Finally, you will determine the relationship between angle relationships and how they determine if two lines are parallel or perpenidcular.
3.1 Parallel lines do not intersect and they lie in the same plane (coplanar). Skew lines do not intersect and are in different planes (not coplanar). Angle pairs formed by two lines cut by transversal include corresponding angles, alternate interior angles, consecutive interior angles, and alternate exterior angles.
Vocabulary and NOTES: parallel lines, parallel planes, skew lines, transversal, interior angles, exterior angles, consecutive interior angles, alternate interior/exterior angles and corresponding angles.
Level of understanding for this section:
3.2 If you have two parallel lines cut by a transversal: (1) the pairs of corresponding angles are congruent, (2) the pairs of alternate interior angles are congruent, (3) the pairs of alternate exterior angles are congruent and (4) the pairs of consecutive interior angles are supplementary.
Level of Understanding for this section:
3.3 When two lines are cut by a transversal so that (1) corresponding angles are congruent, (2) alternate interior angles are congruent, (3) alternate exterior angles are congruent, or (4) consecutive interior angles are supplementary, then the lines are parallel. If two lines are parallel to a third line, then they are parallel to each other.
Level of Understanding for this section:
3.4 and 3.5
The slope m of a nonvertical line is the ratio of vertical change (rise) to horizontal change (run) between any two points on the line. Two nonvertical lines are parallel if and only if they have the same slope. Two nonvertical lines are perpendicular if and only if the product of their slopes is –1.
Know how to graph a line. Know three forms of writing an equation for a line:
Point-Slope. Slope Intercept, Standard form
Level of Understanding for this section:
If you know two points on a line, you can calculate the slope m using the slope formula, and you can substitute the slope and one ordered pair into the slopeintercept form y = mx + b to find b, the y-intercept. Then you can write the slopeintercept form of the equation of the line. Check that the equation is correct by graphing.

3.6 Two lines that intersect to form a linear pair of congruent angles are perpendicular. Perpendicular lines form four right angles. In a plane, a transversal perpendicular to one of two parallel lines is perpendicular to the other. Two lines perpendicular to the same line are parallel to each other. The distance from a point to a line is the length of the perpendicular segment from the point to the line.
SOME ADDITIONAL INFORMATION (IN NO PARTICULAR ORDER)
Level of Understanding for this section:
PARALLEL LINES AND TRANSVERSALS
Coplanar lines that do not intersect are called parallel lines. Planes that do not intersect are called parallel planes. The notation // is used to show parallelism. Non-coplanar lines (lines that are not parallel and do not intersect) are called skew lines.
This diagram shows skew lines.
A line that intersects two or more lines in a plane at different points is called a transversal.
The intersection of these lines creates a variety of angle relationships. Each intersection creates four angles. Each angle has a corresponding angle at the other intersection.
When a transversal intersects a pair of parallel lines, the corresponding angles are congruent. This postulate is called the Corresponding angles postulate (CAP). In this same situation, alternate interior angles and alternate exterior angles are congruent.
Furthermore, each pair of consecutive interior angles is supplementary.

KNOW HOW TO CONSTRUCT
PERPENDICULAR LINES AND HOW
TO CONSTRUCT PARALLEL LINES.
Do this on a separate sheet of paper and attach.
Draw a picture of that here.
Because parallel lines create pairs of angles with special relationships, those pairs of angles can be used to prove that lines are parallel. Know the conditions that verify that lines are parallel are: (Name all ways to show lines are parallel here)
Write the standard form of an equation in this box. Then state the slope and y-intercept.

Any additional information needed for success in this chapter: (especially from lesson 3.6)
END OF CHAPTER BONUS ASSIGNMENT.
Worth 15 additional points in the homework grade for quarter.
This research paper should not be more than one page typed. You must present this project to me on a piece of construction paper or poster board and it is due before
October 24th, 2014.

Section Number and
Topic
3.1 Identify Pairs of
Lines and Angles
Standards Learning Target
MAFS.912.G.CO.1
Will identify angle pairs formed by three intersecting lines.
Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circle arc.
Assignments
PAGE 142 #1,3-32, 43,44
3.2 Use Parallel Lines and Transversals
MAFS.912.G.CO.9
Will use angles formed by parallel lines and transversals.
Prove theorems about lines and angles.
3.3 Prove Lines
Parallel
3.4 Find and Use
Slopes of Lines
3.5 Write and Graph
Equations of Lines
3.6 Prove Theorems about Perpendicular
Lines
MAFS.912.G.CO.9
Will use angle relationships to prove that lines are parallel.
Prove theorems about lines and angles.
MAFS.912.G.GPE.5
Will find and compare slopes of lines.
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems
(e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
MAFS.912.G.GPE.5
Will find equations of lines.
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems
(e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
MAFS.912.G.CO.9
Will find the distance between a point and a line.
Prove theorems about lines and angles.
PAGE 149 #3-8, 20, 25-36
PAGE 167 #2-7, 11-14, 21-
23,26,30-34, 39,40
PAGE 176 #3-19 ODD, 22,
23-35 ODD, 45,
48,49,52,57,58,63,65
PAGE 157 #2, 4-8 even, 9-15,
17, 20-24, 27-31, 34,35
PAGE 186 # 1,13,14,22,24,35-
38