6th Grade Math Textbook, Progress

Update your skills. See page 18.

Angles of Parallel Lines

10-4

A line that intersects two or more lines at different points is

called a transversal. In many cases, those lines are parallel.

In the figure at the right, AB and CD are

intersected by transversal t.

The interior angles are 
 3 , 
 4 , 
 5 , and 
 6.

The exterior angles are 
 1 , 
 2 , 
 7 , and 
 8.

Special names are given to the pairs of angles

formed by the transversal.

Corresponding angles are a pair of nonadjacent Corresponding angles:

angles, one interior and one exterior, that are 
 1 and 
 5 ; 
 2 and 
 6 ;

both on the same side of the transversal. 
 3 and 
 7 ; 
 4 and 
 8.

Corresponding angles of parallel lines So, 
 1 

 5 , 
 2 

 6 , 
 3 

 7 ,

are congruent. and 
 4 

 8.

Alternate interior angles are a pair of Alternate interior angles:

nonadjacent interior angles on opposite 
 3 and 
 6 ; 
 4 and 
 5.

sides of the transversal.

Alternate interior angles of parallel lines So, 
 3 

 6 and 
 4 

 5.

are congruent.

Alternate exterior angles are a pair of Alternate exterior angles:

nonadjacent exterior angles on opposite 
 1 and 
 8 ; 
 2 and 
 7.

sides of the transversal.

Alternate exterior angles of parallel lines So, 
 1 ≅
 8 and 
 2 ≅
 7.

are congruent.

Study this example.

In the figure, 
nand m
 1 
40°. Find the measure of each indicated angle.

a. m
 2 
140° 
1 and 
2 are supplementary.

b.m
 3 
40° 
1 and 
3 are vertical angles.

c. m
 5 
40° 
3 and 
5 are alternate interior angles.

d.m
 6 
140° 
2 and 
6 are corresponding angles.

e. m
 7 
40° 
1 and 
7 are alternate exterior angles.




A

t

B

C D

1 2

3 4

5 6

7 8



n

t

1 2

3

5 6

7

4

8

ABCD




8206-2_336-337 10/7/07 11:51 AM Page 336