Transcript Chapter 3 Notes - Illini West High School

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 Notes
Parallel 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
Alternate Interior Angles
Alternate Exterior Angles
Consecutive Interior Angles
(Same-Side Int. Angles)
1 2
3 4
5 6
7 8
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 Notes
Corresponding ∠ Thm
Alt. Int. ∠ Thm
Alt. Ext. ∠ Thm
Same-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 Notes
Four 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 Notes
Thm – If 2 lines are parallel to the same line
then they are parallel to each other.
p q r
* If p II q and q II r, then p II 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 Notes
Triangle 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
Run
m = y – y1
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