Transcript Theorems about Parallel Lines

Chapter 3 Perpendicular & Parallel Lines
Sec. 3.1 Lines and Angles
GOALS:
To identify relationships between lines
and angles formed by transversals
Vocabulary
Perpendicular lines – two lines that intersect to form a right
angle.
h
k h
k
Parallel lines – two lines that are coplanar and do not
intersect.
k h
h
d
k
P
Vocabulary Cont.
Skew lines – lines that do not intersect and are not
coplanar.
l
m
Parallel Postulate
There is exactly one line through P parallel to l
.
P
l
Vocabulary Cont.
Perpendicular Postulate
There is exactly one line through P perpendicular to l
.
P
l
Transversal
Transversal - a line that intersects two or more coplanar lines.
Eight angles are formed.
t
2
4
6
8
5
7
1
3
Special Angles Names
(for two lines cut by a transversal)
Corresponding angles - those in the same position on each
line in relation to the transversal.
2
4
1
3
1 and 5
2 and 6
6
8
5
7
3 and 7
4 and 8
Special Angles Names Cont.
(for two lines cut by a transversal)
Alternate interior angles - they alternate (cross over )
the transversal and are inside the two lines
4 and 5
4
6
5
3
3 and 6
Special Angles Names Cont.
(for two lines cut by a transversal)
Alternate exterior angles - on opposite sides of the
transversal and are outside the two lines
2
1
1 and 8
2 and 7
8
7
Special Angles Names Cont.
(for two lines cut by a transversal)
Consecutive interior angles - on the same side of the
transversal and are inside the two lines)
3 and 5
4
6
5
3
4 and 6
Example
What kind of angles are angles 4 and 5?
k
h
5
t
4
Example
What kind of angles are angles 11 and 12?
t
k
12
11
h
Example
What kind of angles are angles 11 and 12?
t
12
k
11
h
Example
List all pairs of: Alternate Exterior Angles
Alternate Interior Angles
Corresponding Angles
Consecutive Interior Angles (same-side interior)
Vertical Angles
Linear Pairs
1 2
5 6
3 4
7 8