1. PARALLEL LINES CUT BY A TRANSVERSAL

2. DEFINITIONS PARALLEL TRANSVERSAL ANGLE VERTICAL ANGLE
CORRESPONDING ANGLE
ALTERNATE INTERIOR ANGLE
ALTERNATE EXTERIOR ANGLE

3. DEFINITIONS
SUPPLEMENTARY ANGLE
COMPLEMENTARY ANGLE
CONGRUENT

4. Some special angles you need to know
Linear Pair
These angles are adjacent and supplementary. 1 2

5. One more special angle Vertical angles
Vertical angles form two sets of opposite rays.
They are always congruent. 4 3

6. Parallel lines cut by a transversal2 1 3 4 6 5 7 8

7. Parallel lines cut by a transversal2 1 3 4 6 5 7 8
< 1 and < 2 are called SUPLEMENTARY ANGLES
They form a straight angle measuring 180 degrees.

8. Parallel lines cut by a transversal2 1 3 4 6 5 7 8
< 2 and < 3
< 3 and < 4
< 4 and < 1
< 5 and < 6
Name other supplementary pairs:
< 6 and < 7
< 7 and < 8
< 8 and < 5

9. Parallel lines cut by a transversal2 1 3 4 6 5 7 8
< 1 and < 3 are called VERTICAL ANGLES
They are congruent m<1 = m<3

10. Parallel lines cut by a transversal2 1 3 4 6 5 7 8
< 2 and < 4
< 6 and < 8
Name other vertical pairs:
< 5 and < 7

11. Parallel lines cut by a transversal2 1 3 4 6 5 7 8
< 1 and < 5 are called CORRESPONDING ANGLES
They are congruent m<1 = m<5
Corresponding angles occupy the same position on the top and bottom parallel lines.

12. Parallel lines cut by a transversal2 1 3 4 6 5 7 8
< 2 and < 6
< 3 and < 7
Name other corresponding pairs:
< 4 and < 8

13. Parallel lines cut by a transversal2 1 3 4 6 5 7 8
< 4 and < 6 are called ALTERNATE INTERIOR ANGLES
They are congruent m<4 = m<6
Alternate Interior on on the inside of the two parallel lines and on opposite sides of the transversal.

14. Parallel lines cut by a transversal2 1 3 4 6 5 7 8
< 3 and < 5
Name other alternate interior pairs:

15. Parallel lines cut by a transversal2 1 3 4 6 5 7 8
< 2 and < 8
< 1 and < 7
Name other alternate exterior pairs:

16. TRY IT OUT 2 1 3 4 6 5 7 8 120 degrees The m < 1 is 60 degrees.
What is the m<2 ?
120 degrees

17. TRY IT OUT 2 1 3 4 6 5 7 8 60 degrees The m < 1 is 60 degrees.
What is the m<5 ?
60 degrees

18. TRY IT OUT 2 1 3 4 6 5 7 8 60 degrees The m < 1 is 60 degrees.
What is the m<3 ?
60 degrees

19. TRY IT OUT
120 60 60
120
120 60 60
120

20. TRY IT OUT 2x + 20 x + 10 What do you know about the angles?
Write the equation.
Solve for x.
SUPPLEMENTARY
2x x + 10 = 180
3x + 30 = 180
3x = 150
x = 30

21. TRY IT OUT 3x - 120 2x - 60 What do you know about the angles?
Write the equation.
Solve for x.
ALTERNATE INTERIOR
3x = 2x - 60
x =
Subtract 2x from both sides
Add 120 to both sides