Objective: identify pairs of angles formed by transversals
Transversal
A transversal is a line that intersects two coplanar
lines at two distinct points.
Examples:
t
t
Counterexample:
t
t
Corresponding Angles
Consider the examples and counterexample below
and write a definition for corresponding angles.
Examples:
t
t
1
t
2
6
5
3
7
Counterexample:
t
4
7
Corresponding Angles
Definition:
Alternate Interior Angles
Consider the examples and counterexample below
and write a definition for alternate interior angles.
Examples:
t
t
3
Counterexample:
4
5
6
t
4
6
Alternate Interior Angles
Definition:
Alternate Exterior Angles
Definition:
Label a pair of alternate exterior angles.
t
Same-Side Interior Angles
Consider the examples and counterexample below
and write a definition for same-side interior angles.
Examples:
t
t
1
2
8
Counterexample:
t
2
8
7
Same-Side Interior Angles
Definition:
Same-Side Exterior Angles
Definition:
Label a pair of same-side exterior angles.
t
Identifying Angles
Find all pairs of corresponding angles in the
diagram.
(Hint: There are 4 pairs of corresponding angles.)




Identifying Angles
Find all pairs of alternate interior angles in the
diagram.
(Hint: There are 2 pairs of alternate interior angles.)


Identifying Angles
Find all pairs of alternate exterior angles in the
diagram.
(Hint: There are 2 pairs of alternate interior angles.)


Identifying Angles
Find all pairs of same-side interior angles in the
diagram.
(Hint: There are 2 pairs of same-side interior angles.)


Identifying Angles
Find all pairs of same-side exterior angles in the
diagram.
(Hint: There are 2 pairs of same-side interior angles.)


Identifying Angles
You will see two angles marked on a diagram
 If you think they are vertical angles, write V.
 If you think they are corresponding angles, write C.
 If you think they are alternate interior angles, write AI.
 If you think they are alternate exterior angles, write AE.
 If you think they are same-side interior angles, write SI.
 If you think they are same-side exterior angles, write SE.
Vertical Angles
Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
Same-Side Interior Angles
Same-Side Exterior Angles
Vertical Angles
Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
Same-Side Interior Angles
Same-Side Exterior Angles
Vertical Angles
Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
Same-Side Interior Angles
Same-Side Exterior Angles
Vertical Angles
Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
Same-Side Interior Angles
Same-Side Exterior Angles
Vertical Angles
Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
Same-Side Interior Angles
Same-Side Exterior Angles
Vertical Angles
Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
Same-Side Interior Angles
Same-Side Exterior Angles
Vertical Angles
Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
Same-Side Interior Angles
Same-Side Exterior Angles
Vertical Angles
Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
Same-Side Interior Angles
Same-Side Exterior Angles
Vertical Angles
Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
Same-Side Interior Angles
Same-Side Exterior Angles
Vertical Angles
Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
Same-Side Interior Angles
Same-Side Exterior Angles
Assignment
Section 4.5 (One Problem Set) #1-5