1. Angles and Parallel Lines2 1 4 3
Angles and Parallel Lines 6 5 8 7

2. When a transversal t intersects line n and m, EIGHT angles are formed
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 are formed
Exterior angles: Outside the lines
Interior angles : Between the lines t m n

3. Vertical Angles & Linear Pair
Two angles that are opposite angles.
Vertical angles are congruent.
 1   4,  2   3,  5   8,  6   7
Supplementary angles that form a straight line (sum = 180)
1 & 2 , 2 & 4 , 4 &3, 3 & 1,
5 & 6, 6 & 8, 8 & 7, 7 & 5 1 2 3 4 5 6 7 8

4. Corresponding Angles
Corresponding Angles: Two angles, on the same side of the transversal, that occupy corresponding positions, one interior and one exterior.
 2 and  6,  1 and  5,  3 and  7,  4 and  8 1 2 3 4 5 6 7 8

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

6. Consecutive Angles
Consecutive Interior Angles: Two angles that lie between the lines, both on the same side of the transversal.
Consecutive Exterior Angles: Two angles that lie outside the lines, both on the same side of the transversal.
3 and 5 , 4 and 6
1 and 7 , 2 and 8 1 2 3 4 5 6 7 8

7. Example List all pairs that fit the description Corresponding
Alternate Exterior
Alternate Interior
Consecutive Interior
< 4 and < < 3 and < < 5 and < < 6 and < 8
< 4 and < < 1 and < 5
< 2 and < < 3 and < 7
< 3 and < < 6 and < 7

8. Example
Complete the statement with corresponding, alternate exterior, alternate interior, or consecutive interior.
< 4 and < 8 are
< 2 and < 6 are
< 1 and < 8 are
< 7 and < 2 are
< 4 and < 6 are
< 5 and < 7 are
Alternate interior
Alternate exterior
Consecutive interior
Consecutive exterior
Corresponding
Vertical

9. Investigation Let’s check out the relationship of these angle pairs!

10. Angles and Parallel Lines
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

11. Example
Given a ll b, find each measure given that m < 6 = 67°.

12. Example
State the postulate or theorem that justifies the statement.

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. t 16 15 14 13 12 11 10 9 8 7 6 5 3 4 2 1 s D C B A
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°

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. t 16 15 14 13 12 11 10 9 8 7 6 5 3 4 2 1 s D C B A
ANSWERS:
1. 30
2. 35
3. 33