CHAPTER 3
CHAPTER
REVIEW
Relationships Between Lines:
GOAL: Identify relationships between lines
Two lines are parallel lines if they lie in the same plane and do not intersect.
Two lines are perpendicular lines if they intersect to form a right angle.
p
m
n
q
Two lines are skew lines if they do not lie in the same plane.
Skew Lines never intersect.
c
b
●
A
All segments in the diagram
are part of a line and all
corners of the cube form
right angles.
Name a line that is
skew to VW.
R
Q
U
W
Name a plane that appears
parallel to plane VWX.
Name a line that is
perpendicular to plane VWX.
V
S
T
X
THEOREMS ABOUT PERPENDICULAR LINES:
GOAL: Use theorems about perpendicular lines
Theorem 3.1
Words: All right angles are congruent.
Symbols: If the m A = 90° and m B = 90°,
then
A
B
A
B
Theorem 3.2
Words:
If two lines are perpendicular, then
they intersect to form four right angles.
Symbols: If n
m, then m 1 = 90°, m
m 3 = 90°, and m 4 = 90°.
2 = 90°,
1
4
3
2
Theorem 3.3
Words:
If two lines intersect to form
adjacent congruent angles, then
the lines are perpendicular.
●
B
A
1
2
Symbols: If
1
2, then AC
BD
●
D
●
C
Theorem 3.4
Words:
If two sides of adjacent acute angles
are perpendicular, then the angles are
complementary.
F●
●G
3
Symbols: If EF
EH, then m
3+m
4 = 90°
●
E
4
●
H
In the diagram at the right,
EF
EH and m GEH = 30 °.
Find the value of y.
F●
E●
2y – 12
30°
●
G
●
H
1. Name a pair of alternate interior angles
2. Name a pair of corresponding angles.
3. Name a pair of same-side interior angles.
4. Name a pair of alternate exterior angles.
1 3
2 4
5 7
6 8
If j ǁ k then find:
1.
2.
3.
4.
5.
6.
7.
m<1
m<2
m<3
m<4
m<5
m<6
m<7
72°
1
2
≫
3
4 5
6
7
≫
j
k
120°
≫
2x + 32
≫
Solve for x.
≫
45°
3x – 15
Solve for x.
≫
74°
≫
5x + 14
Solve for x.
≫
103°
6y – 23
Solve for y.
≫
≫
Showing Lines are Parallel
Goal:
Show that two lines are parallel.
The converse of an if-then statement is the statement formed by
switching the hypothesis and the conclusion.
Write the converse for the given if-then statement:
1. If two angles have the same measure, then the two angles are congruent.
Examples:
Determine the postulate that proves the lines are parallel.
1.
63°
2.
55°
125°
63°
138°
3.
4.
138°
56°
56°
5.
145°
145°
Theorem 3.11
Words:
If two lines are parallel to the same line,
then they are parallel to each other.
Symbols: If q ǁ r and r ǁ s, then q ǁ s.
q
r
s
Theorem 3.12
Words:
In a plane, if two lines are perpendicular to the same line,
then they are parallel to each other.
Symbols: If m
p and n p then m ǁ n.
m
n
p
Determine whether if the given picture is a translation.
1.
3.
2.
4.
PRACTICE
PAGE 160-163
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