Download Transversal

Parallel Lines
&
Transversals
&
Angles
Transversal
Definition:.
A line, ray, or segment that intersects 2 or more
COPLANAR lines, rays, or segments.
Parallel
lines
transversal
NonParallel
lines
transversal
Vertical Angles & Linear Pair
Vertical Angles: Two angles that are opposite angles. Vertical
angles are congruent.
 1   4,  2   3,  5   8,  6   7
Linear Pair: Supplementary angles that form a line (sum = 180)
1 & 2 , 2 & 4 , 4 &3, 3 & 1,
5 & 6, 6 & 8, 8 & 7, 7 & 5
1
2
3 4
5
7
6
8
Transversals, Angles and Parallel
Lines
3
INTERIOR
–The space INSIDE the 2
lines
interior
EXTERIOR
-The space OUTSIDE the 2
lines
exterior
exterior
Lesson 2-4: Angles and Parallel
Lines
5
Transversals, Angles and Parallel
Lines
6
Transversal

When a transversal t intersects line n and m, eight angles
of the following types are formed:
Exterior angles
Interior angles
Consecutive interior angles
Alternative exterior angles
Alternative interior angles
Corresponding angles
m
t
n
Lesson 2-4: Angles and Parallel
Lines
7
Special Angle Relationships
Interior Angles
1 2
3 4
<3 & <6 are Alternate Interior angles
<4 & <5 are Alternate Interior angles
<3 & <5 are Same Side Interior angles
<4 & <6 are Same Side Interior angles
5 6
7 8
Exterior Angles
<1 & <8 are Alternate Exterior angles
<2 & <7 are Alternate Exterior angles
<1 & <7 are Same Side Exterior angles
<2 & <8 are Same Side Exterior angles
Special Angle Relationships
WHEN THE LINES ARE PARALLEL
1 2
3 4
5 6
7 8
If the lines are not
parallel, these angle
relationships DO NOT
EXIST.
♥Alternate Interior Angles
are CONGRUENT
♥Alternate Exterior Angles are
CONGRUENT
♥Same Side Interior Angles are
SUPPLEMENTARY
♥Same Side Exterior Angles are
SUPPLEMENTARY
Angles and Parallel Lines

1.
2.
3.

1.
2.
If two parallel lines are cut by a transversal, then the
following pairs of angles are congruent.
Corresponding angles
Alternate interior angles
Alternate exterior angles
If two parallel lines are cut by a transversal, then the
following pairs of angles are supplementary.
Consecutive interior angles
Consecutive exterior angles
Continued…..
Lesson 2-4: Angles and Parallel
Lines
10
Corresponding Angles & Consecutive Angles
Corresponding Angles: Two angles that occupy
corresponding positions.
 2   6,  1   5,  3   7,  4   8
1
3
2
4
5 6
7 8
Lesson 2-4: Angles and Parallel
Lines
11
Consecutive Angles
Consecutive Interior Angles: Two angles that lie between parallel
lines on the same sides of the transversal.
m3 +m5 = 180º, m4 +m6 = 180º
Consecutive Exterior Angles: Two angles that lie outside parallel
lines on the same sides of the transversal.
1
m1 +m7 = 180º, m2 +m8 = 180º
3
4
5
7
Lesson 2-4: Angles and Parallel
Lines
2
6
8
12
Alternate Angles

Alternate Interior Angles: Two angles that lie between parallel
lines on opposite sides of the transversal (but not a linear pair).
 3   6,  4   5

Alternate Exterior Angles: Two angles that lie outside parallel
lines on opposite sides of the transversal.  2   7,  1   8
1
3
4
5
7
2
6
8
Lesson 2-4: Angles and Parallel
Lines
13
Example: If line AB is parallel to line CD and s is parallel to t, find
the measure of all the angles when m< 1 = 100°. Justify your answers.
A
1
4
C
5
8
m<2=80° m<3=100° m<4=80°
2
12
3
6
10
11
t
m<5=100° m<6=80° m<7=100° m<8=80°
m<9=100° m<10=80° m<11=100° m<12=80°
m<13=100° m<14=80° m<15=100° m<16=80°
Lesson 2-4: Angles and Parallel
Lines
B
D
13 14
16 15
7
s
9
14
Example: If line AB is parallel to line CD and s is parallel to t, find:
1. the value of x, if m<3 = 4x + 6 and the m<11 = 126.
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.
ANSWERS:
1. 30
1
A
4
C
5
8
2. 35
2
12
3
6
3. 33
Lesson 2-4: Angles and Parallel
Lines
B
10
11
D
13 14
16 15
7
s
9
t
15
Let’s Practice
1201 2 60
°
°
60 3 4
120
°
120 5 660°
° 7 8 °
120
60
°
°
m<1=120°
Find all the remaining
angle measures.
Another practice problem
40
°
120°
Find all the missing
angle measures,
and name the
postulate or
theorem that
gives us
permission to
make our
statements.
Assignment
Section 3.1
Page 147