Angles and
Parallel Lines
1
Lesson 2-4: Angles and Parallel
Lines
2
Transversal
l
Definition: A line that intersects two or more lines in a
plane at different points is called a transversal.
l
When a transversal t intersects line n and m, eight angles
of the following types are formed:
m
Exterior angles
Interior angles
Consecutive interior angles
Alternative exterior angles
Alternative interior angles
Corresponding angles
t
n
Lesson 2-4: Angles and Parallel
Lines
3
Vertical Angles & Linear Pair
Vertical Angles: Two angles that are opposite angles. Vertical
angles are congruent.
Ð 1 @ Ð 4, Ð 2 @ Ð 3, Ð 5 @ Ð 8, Ð 6 @ Ð 7
Linear Pair: Supplementary angles that form a line (sum = 180°)
Ð1 & Ð2 , Ð2 & Ð4 , Ð4 &Ð3, Ð3 & Ð1,
Ð5 & Ð6, Ð6 & Ð8, Ð8 & Ð7, Ð7 & Ð5
1 2
3 4
5 6
7 8
Lesson 2-4: Angles and Parallel
Lines
4
Angles and Parallel Lines
l
1.
2.
3.
l
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
5
Corresponding Angles & Consecutive Angles
Corresponding Angles: Two angles that occupy
corresponding positions.
Ð 2 @ Ð 6, Ð 1 @ Ð 5, Ð 3 @ Ð 7, Ð 4 @ Ð 8
1 2
3 4
5 6
7 8
Lesson 2-4: Angles and Parallel
Lines
6
Consecutive Angles
Consecutive Interior Angles: Two angles that lie between parallel
lines on the same sides of the transversal.
mÐ3 +mÐ5 = 180º, mÐ4 +mÐ6 = 180º
Consecutive Exterior Angles: Two angles that lie outside parallel
lines on the same sides of the transversal.
1
mÐ1 +mÐ7 = 180º, mÐ2 +mÐ8 = 180º
3
2
4
5 6
7 8
Lesson 2-4: Angles and Parallel
Lines
7
Alternate Angles
l
Alternate Interior Angles: Two angles that lie between parallel
lines on opposite sides of the transversal (but not a linear pair).
Ð 3 @ Ð 6, Ð 4 @ Ð 5
l
Alternate Exterior Angles: Two angles that lie outside parallel
lines on opposite sides of the transversal. Ð 2 @ Ð 7, Ð 1 @ Ð 8
1 2
3 4
5 6
7 8
Lesson 2-4: Angles and Parallel
Lines
8
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.
1
A
4
C
5
8
m<2=80
m<3=100
m<5=100
m<6=80
m<9=100
m<10=80
m<13=100
m<14=80
m<4=80
m<7=100
m<11=100
m<15=100
2
12
3
6
B
10
11
D
13 14
16 15
7
s
9
t
m<8=80
m<12=80
m<16=80
Lesson 2-4: Angles and Parallel
Lines
9
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
4
C
5
8
2. 35
3. 33
1
A
2
12
3
6
Lesson 2-4: Angles and Parallel
Lines
B
10
11
D
13 14
16 15
7
s
9
t
10