Chapter 3.1

Common Core G.CO.1 & G.CO.9 Know precise definitions of…parallel line. Prove theorems about lines and angles.

Objectives – To identify relationships between figures in space. To identify angles formed by two lines and a transversal.

Ch 3.1 NotesParallel Lines – 2 lines that do not intersect and are coplanar

Parallel Planes – 2 planes that do not intersect

Skew Lines – 2 lines that do not intersect and are not coplanar

Identifying Angles Formed by Transversals

Transversal – is a line that intersects 2 or more coplanar lines at different points. Transversal

Corresponding Angles 1 2

3 4

Alternate Interior Angles 5 6

7 8

Alternate Exterior Angles

Consecutive Interior Angles(Same-Side Int. Angles)

Chapter 3.2

Common Core G.CO.9 Prove theorems about lines and angles. Theorems include…when a transversal crosses parallel lines, alternate interior angles are congruent.

Objectives – To prove theorems about parallel lines. To use properties of parallel lines to find angles measures.

Ch 3.2 NotesCorresponding ∠ ThmAlt. Int. ∠ ThmAlt. Ext. ∠ ThmSame-Side Int. ∠ Post.(Consecutive Int. Post.)

Chapter 3.3

Common Core G.CO.9 Prove theorems about lines and angles. Theorems include…when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent.

Objective – To determine whether two lines are parallel.

Ch 3.3 NotesFour ways to prove two lines are parallel.

1) Show Corr. ∠’s are ≌2) Show Alt. Int. ∠’s are ≌3) Show Alt. Ext. ∠’s are ≌4) Show Same Side are Supp. (Cons. Int. ∠’s are supp.)

Flow Proof – is another way of proving something by using arrows and logically connections between statements

Chapter 3.4

Common Core Common Core G.MG.3 Apply geometric methods to solve design problems.

Objective – To relate parallel and perpendicular lines.

Ch 3.4 NotesThm – If 2 lines are parallel to the same line

then they are parallel to each other.* If p II q and q II r, then p II r. p q r

Thm – In a plane, if 2 lines are perpendicular to the same line, then they are parallel to each other.

* If m ⊥ p and n ⊥ p, then m II n.

Perpendicular Transversal Thm – If a transversal is perpendicular to one of 2 parallel lines, then it is perpendicular to the other.

If then

Chapter 3.5

Common Core Common Core G.CO.10 Prove theorems about triangles…measures of interior angles of a triangle sum to 180 degrees.

Objectives – To use parallel lines to prove a theorem about triangles. To find measures of angles of triangles.

Ch 3.5 NotesTriangle Angle-Sum Theorem – the sum of the measures of the angles of a triangle is 180.

Triangle Exterior Angle Theorem – the measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles

Parallel Postulate – 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.

If then

Chapter 3.6

Common Core G.CO.12 & G.CO.13 Make formal geometric constructions with a variety of tools and methods…constructing perpendicular lines…and constructing a line parallel to a given line through a point not on the line.

Objective – To construct parallel and perpendicular lines.

Ch 3.6 Notes

Constructing Parallel Lines

Construct a Special Quadrilateral with one pair of parallel sides.

Construct a Perpendicular at a Point on the Line

Perpendicular Postulate – If there is a line and a point not on the line then there is exactly one line through the point and perpendicular to the given line

If then

Construct a Perpendicular form a Point to Line

Chapter 3.7

Common Core G.GPE.5 Prove the slope criteria for parallel and perpendicular lines.

Objective – To graph and write linear equations.

Ch 3.7 Notes

Slope = Rise m = y – y1

Run x – x1

Slope-intercept Form – y = mx + b where m is the slope and b is the y-intercept

Point-Slope Form – y – y1 = m(x – x1) where m is the slope and (x1,y1) is the point

Chapter 3.8

Common Core G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.

Objective – To relate slope to parallel and perpendicular lines.

Ch 3.8 Notes 2 Lines are Parallel to each other if they have

the same slope.Ex. m = -4 and m1 = -4

2 Lines are Perpendicular to each other if their slopes are negative reciprocals of each other.

Ex. m = 2/3 and m1 = -3/2 then they would be perpendicular lines