Section 3.1
Lines and Angles
Perpendicular Lines
• Intersecting lines that form right angles
• Symbol
XS
SR
Parallel Lines
• Two lines that are coplanar and do not
intersect
• Symbol: II
XY II UZ
Skew Lines
• Lines do not intersect and are not coplanar
Example
• Is XY parallel or skew to RV?
XY II
RV
Parallel planes
• Two planes that do not intersect
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.
Perpendicular Postulate
• If there is a line and a point not on the line,
then there is exactly one line through the
point perpendicular to the given line.

Theorem 3.1
• If two lines intersect to form a linear pair of
congruent angles, then the lines are
perpendicular
m<ABD = m<DBC and a
• Ex 1
D
A
B
linear pair, BD
C
AC
Theorem 3.2
• If two sides of two adjacent acute angles
are perpendicular, then the angles are
complementary.
• Ex. 2
F
J
<FGJ is complementary to <JGH
G
H
Examples: Solve for x
Ex 3.
x
60°
ANSWER: 60 + x = 90
-60
-60
x = 30
Example 4
ANSWER:
x + 55 = 90
-55
x
55°
-55
x = 35
Example 5
ANSWER:
2x – 9 + 27 = 90
2x +18 = 90
27°
(2x-9)°
2x = 72
x = 36
Theorem 3.3
• If 2 lines are perpendicular, then they
intersect to form four right angles.
l
m
Complete
Try it! Problems
#1-8
Transversal
• A line that intersects two or more coplanar
lines at different points.
transversal
Vertical Angles
• Formed by the intersection of two pairs of
opposite rays
1
3
7
4
6
5
8
2
Linear Pair
• Adjacent angles that are supplementary
1
3
7
4
6
5
8
2
Corresponding Angles
• Occupy corresponding positions.
1
3
7
4
6
5
8
2
Alternate Exterior Angles
• Lie outside the 2 lines on opposite sides of
the transversal.
1
3
7
4
6
5
8
2
Alternate Interior Angles
• Lie between the 2 lines on opposite sides
of the transversal.
1
3
7
4
6
5
8
2
Consecutive Interior Angles
(Same side interior angles)
• Lie between the 2 lines on the same side
of the transversal.
1
3
7
4
6
5
8
2
Angle Relationships:
Name a pair of angles
• Corresponding
1
– Ex. 1 & 5
3
• Alternate Exterior
– Ex. 2 & 7
• Alternate Interior
– Ex. 4 & 5
• Consecutive Interior
– Ex. 3 & 5
5
7
6
8
2
4