Download Geometry Cornell Notes-Chapter 3

Geometry
Chapter 3: Parallel and Perpendicular Lines
objectives:
3.1 Parallel Lines and
-identify the relationships between two lines or two planes
Transversals
-name angles formed by a pair of lines and a transversal
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Bell Ringer
Answer question on transparency. Show work here and circle your final answer:
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Parallel lines PQ  RS or l  m
Parallel planes
a. Name all planes that are parallel to plane ABD.
b. Name all segments that are parallel to CG .
c. Define skew lines d. Name all segments that are skew to EH .
e. Define Transversals
Special Angle Pairs formed
by two lines cut by a
transversal:
Alternate interior angles:
Alternate Exterior angles:
Corresponding angles:
Consecutive interior angles:
Consecutive exterior angles:
State the transversal that forms each pair of angles and identify the special
Examples name for the angle pair.
1. 1 and 13
2. 8 and 12
2. 8 and 2
Assignment 3.1 page 129
(draw all diagrams) #22-27
all, 32-46 even
Honors: Additionally, #4951, 53, 54, 56
4. 3 and 2
5. 11 and 9
6. 1 and 15
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Summary Question (complete on back): What do you call a line that intersects
two or more lines in a plane? What types of angles does it create?
1
Geometry
3.2 Angles and Parallel
Lines
Bell Ringer
Activity:
Properties involving parallel
lines cut by a transversal
Objective:
-use the properties of parallel lines to determine congruent angles
-use algebra to find angle measures
Answer question on transparency. Show work here and circle your final answer:
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1. With a ruler, draw two parallel lines on a piece of notebook paper that
are 5-10 line apart
2. Label them l and m
3. Number the angles 1-8
4. Using a protractor, measure each of the angles and write the angle
measures inside the angles
IF
If two parallel lines
are cut by a
transversal,
THEN
1. corresponding angles are _____
2. alt. interior angles are _____
3. alt. exterior angles are _____
4. cons. interior angles are _____
5. cons. exterior angles are _____
Examples a. Find the measures of the missing angles.
r
7
135°
1
t
3
4
2
5
6
b. Find the measures of the missing angles.
Q
R
70°
50°
2
Geometry
c. In the diagram,
1
2
3
If m1 = 2x + 44 and m5 = 5x + 38. Find m4.
l
4
5
6
7
8
m
d. Find x, y and z.
In a plane, if a line is perpendicular to one of two parallel lines, then it is
Perpendicular Transversal perpendicular to the other.
Theorem
If given a line and a point not on the line, then there exists exactly one line
Parallel Postulate through the point that is parallel to the given line
Find m1.
Example
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Restate the properties involving parallel lines cut by a transversal.
Summary:
Assignment page 136 #1125,32,33,36 (draw diagrams)
3
Geometry
objective:
-find the slope of a line
-use a slope to decide if two lines are parallel, perpendicular or neither
3.3 Slopes of Lines
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Bell Ringer:
Answer question on transparency. Show work here and circle your final answer:
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Slope The ratio of a lines vertical rise to its horizontal run
y 2  y1
x2  x1
Examples Find the slope of each line.
Formula for slope of a line
m
What is the slope of a vertical line?
What is the slope of a horizontal line?
Postulate 3.2 Two lines have the same slope if and only if they are parallel.
Postulate 3.3 Two lines are perpendicular if and only if the product of their slopes is -1.
Examples Determine whether AB and MN are parallel, perpendicular, or neither.
1. A(0,3), B(5,-7), M(-6,7), N(-2,-1) 2. A( -1, 4), B(2, -5), M(-3, 2), N(3, 0)
3. A(-4, -8), B(4, -6), M(-3, 5), N(-1, -3)
Graph the line that satisfies each condition.
4. slope =3, contains A(0,1) 5. slope = 3/2, contains R(- 4, 5)
Summary (on back):
Assignment 3.3 page 142
How
do
you
use
slope
to
determine
if
lines
are
parallel
or
perpendicular?
#16-36 even
4
Geometry
3.4 Equations of Lines
objective:
-write equations in point-slope and slope intercept form
Why Learn This?
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Slope –Intercept Form
Point-Slope Form
The slope intercept form of an equation is y = mx + b.
The point slope form of an equation is y  y1  m( x  x1 ) .
Examples Write equations in point-slope form and slope-intercept form of the line
having the given slope and containing the given point.
1. m: 2, (5, 2)
2. m: -3, (2, -4)
Write an equation in slope-intercept form for each line.
3. r
4. s
5. the line parallel to line r that contains (1, -1)
6. the line perpendicular to line s that contains (0, 0)
Summary:
Assignment 3.4 page 148
Regular: #16-34 even, 45, 54,
55
Honors: #16-42 even, 43-45,
54, 55
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What information is needed to write equations in point slope form?
What information is needed to write equations in slope intercept form?
5
Geometry
Objective:
-Recognize angle conditions that occur with parallel lines
-Prove that two lines are parallel based on given angle relationships
3.5 Proving Lines
Parallel
Bell Ringer:
Answer question on transparency. Show work here and circle your final answer:
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Ways to Prove Lines are
Parallel
IF
Corresponding angles are ,
THEN
the lines are ||
Alternate interior angles are ,
Alternate exterior angles are ,
Consecutive interior angles are
supplementary
Example
Given the following information, determine which lines, if any, are parallel.
State the postulate or theorem that justifies your answer.
1. 3  7
2. 9  11
3. 2  16
4. m5  m12 = 180
Find x so that l || m.
6
Geometry
Example
Assignment 3.5 page 154,
#4-9, 26-31, 34-35, 45, 46
Honors: Additionally, #36,37
Summary
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