Download Chapter 3 Student Notes

Chapter 3
Student Notes
Chapter 3 Test
Friday, October 12 th
3.1
Parallel Lines and Transversals
Parallel Lines
A
C
B
D
Skew Lines and Parallel Planes
 Two lines are skew if they
l
l and m are ________
m
Examples
1.
2.
3.
4.
Name all segments that are parallel to AD
Name all segments that intersect AD
Name all segments that are skew to AD
Name all planes that are parallel to plane ABC.
Answers:
1.
___________________
2.
___________________
3.
___________________
4.
___________________
E
H
G
F
C
D
A
B
Transversal – ___________________________
Exterior Angles – _____________________
Interior Angles – _____________________
1
l
m
2
3 4
5
7
t
6
8
l
m
1 2
3 4
5 6
7 8
t
Consecutive Interior Angles – _____________________
Alternate Exterior Angles –
_____________________
Alternate Interior Angles –
_____________________
Corresponding Angles –
_____________________
q
p
1 2
3 4
8 7
6 5
9 10
11 12
16 17
18 19
r
s
Transversal
1.
2.
3.
4.
5.
3 & 11
11 & 17
17 & 1
2 & 3
4 & 6
Name the transversal that
forms each pair of angles.
Then name the special name
for each pair.
____
____
____
____
____
Special Angle Pair Name
__________________
__________________
__________________
__________________
__________________
3-2
Angles and Parallel Lines
1
m
2
3 4
5
n
6
7
8
t
If m ║ n , then the
following relationships
exists:
1
m
2
3 4
5
n
6
7
8
If m ║ n , then:
t
Corresponding ’s 
Alternate Interior ’s 
Alternate Exterior ’s 
Consecutive Interior ’s supplementary
If m1 = 70o, find the others.
70o
1
2
3
4
5
6
7
8
More Examples
1. The value of x, if
m3 = 4x + 6 and
m11 = 126.
If line AB is parallel to line CD and s is
parallel to t, find:
A
1
4
C
5
8
s
2
3
6
9 10
12 11
13 14
16 15
7
t
2. The value of x, if m1 = 100 and m8 = 2x + 10.
3. The value of y, if m11 = 3y – 5 and m16 = 2y + 20.
B
D
Important Notes:
•When the lines are parallel;
•The acute angles ____________________.
•The obtuse angles ___________________.
•One acute angle is _______________ to one obtuse
angle.
1
m
2
3 4
5 6
7 8
n
t
30o
1
36o
Find the measure of angle 1.
140o
1
30o
Find the measure of angle 1.
Find the value of x and y.
(5x)o
Find x and y.
(8x + 4)0
(6x + 4)0
(6y + 8)0
(5x + 7)0
(2y)0
(5x + 12)0
3-3
Slopes of Lines
Slope of ǁ, and⊥ lines
Determine if each pair of lines are ǁ , ⊥, or neither.
1. Line 1, m = -2
Line 2, m = ½
2. Line 3, m = 3
Line 4, m = 3
3. Line 5, m = 4/3
Line 6, m = 3/4
4. Line 7, m = -1
Line 8, m = 1
Find the slope of each line.
1.
l
2.
m
l
3. Any line ǁ to .
4. Any line ⊥ to
m.
l
m
Slope of a Line
 The slope of the non-vertical line through
the points
and
is
m=
The slope of a vertical line ____________.
The slope of a horizontal line is _______.
Examples
Find the slope of the line through the given
points.
(-4, 7) and (3, 7)
Examples
Find the slope of the line through the given
points.
(3, -1) and (3, 2)
Examples
Find the slope of the line through the given
points.
(1, -4) and (2, 5)
Examples
Find the slope of the line through the given
points.
(-2, 5) and (1, -1)
Given each pair of points, Determine if
AB ǁ CD, AB ⊥ CD, or neither.
1. A(-3, -2) B(9, 1) C(3, 6) D(5, -2)
2. A(5, -4) B(10, 0) C(9, -8) D(5, -13)
m(l) =
m(m) =
m(s) =
m(r) =
l
s
m
r
Graph each line described below.
1. m = 3,
passes through (2, 1)
2. Passes through (-4, -5)
 the line that passes
through MN, M(-1, -3),
N(-3, 4)
m(MN) =
m() =
3-5
Proving Lines Parallel
 If ___________________________________________________
Postulate 3-4
corresponding angles are congruent, then the
_________________.
l
if
m
t
, then ______.
 If ________________________________________________________
Theorem 3-5
alternate exterior angles are congruent, then the
___________________.
l
if
m
t
, then ______.
If __________________________________________________________
consecutive interior angles are supplementary,
Theorem 3-6
then ____________________.
1
if
2
t
l
m
, then ______.
 If ____________________________________________________
alternate interior angles are congruent, then
________________.
Theorem 3-7
l
if
m
t
, then ______.
Theorem 3-8
l
if
m
t
, then ______.
Determine which pair of lines is parallel and why.
s
p
q
1 2
5 6
r
1.  1   8
4
2.  7   12
3
7
8
3.  11   9
9 10
13 14
11 12
15 16
4. m 6 +  10 = 180
Find x so that
(5x +10)o
l
m
110o
l || m
Find x so that
(6x -10)o
l
(5x + 15)o
m
l || m
Find x so that
l
m
l || m
Find x so that
l
m
(7x–1)o
l || m
3.6
Perpendiculars and Distance
How would you measure the distance from
Fishersville to the Beach?
Fishersville
Beach
Draw the segment that represents the distance
from P to AB.
P
A
B
P
A
B
Draw the segment that represents the distance
from P to AB.
P
P
A
B
A
B
Draw the segment that represents the distance
from P to AB.
A
B
B
P
A
P