1. ANGLES FORMED
WHENTWO PARALLEL
LINES ARE CUT BY A
TRANSVERSAL

2. Transversal
•Definition: A line that intersects two or more lines in a plane
at different points is called a 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
t
m
n

3. Corresponding Angles
Corresponding Angles: Two angles that occupy
corresponding positions.
3
 2   6
1 2
3 4
5 6
7 8
 1   5
 3   7
 4   8
The corresponding angles are the ones at the same location
at each intersection

4. Angles and Parallel Lines
• If two parallel lines are cut by a transversal, then the
following pairs of angles are congruent.
1. Corresponding angles
2. Alternate interior angles
3. Alternate exterior angles

5. Proving Lines Parallel
•If two lines are cut by a transversal and corresponding
angles are congruent, then the lines are parallel.
D
C
B
A

6. Alternate Angles
•Alternate Interior Angles: Two angles that lie between parallel
lines on opposite sides of the transversal (but not a linear pair).
•Alternate Exterior Angles: Two angles that lie outside parallel
lines on opposite sides of the transversal.
Lesson 2-4: Angles and Parallel Lines 6
 3   6,  4   5
 2   7,  1   8
1 2
3 4
5 6
7 8

7. 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.
Lesson 2-4: Angles and Parallel Lines 7
m<2=80° m<3=100° m<4=80°
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°
t
16 15
14
13
12 11
10
9
8 7
6
5
3
4
2
1
s
D
C
B
A

8. Proving Lines Parallel
•If two lines are cut by a transversal and alternate interior
angles are congruent, then the lines are parallel.
D
C
B
A

12. Valuing
REFLECTION: (JournalWriting)
Use the quotation below as your guide in giving
an example of situation on how you are going to
apply your significant learnings about properties
of parallel lines in your daily life.
“The road of life twists, turns and no two
directions are ever the same.Yet ourlessons
come from the journey, not the destination’’.