2. PARALLEL LINES CUT BY A TRANSVERSAL

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

4. DEFINITIONS SUPPLEMENTARY ANGLE COMPLEMENTARY ANGLE CONGRUENT

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

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

7. Parallel lines cut by a transversal 12 34 5 6 78

8. 12 34 5 6 78 < 1 and < 2 are called SUPLEMENTARY ANGLES They form a straight angle measuring 180 degrees.

9. Parallel lines cut by a transversal 12 34 5 6 78 Name other supplementary pairs: < 2 and < 3 < 3 and < 4 < 4 and < 1 < 5 and < 6 < 6 and < 7 < 7 and < 8 < 8 and < 5

10. Parallel lines cut by a transversal 12 34 5 6 78 < 1 and < 3 are called VERTICAL ANGLES They are congruent m<1 = m<3

11. Parallel lines cut by a transversal 12 34 5 6 78 Name other vertical pairs: < 2 and < 4 < 6 and < 8 < 5 and < 7

12. Parallel lines cut by a transversal 12 34 5 6 78 < 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.

13. Parallel lines cut by a transversal 12 34 5 6 78 Name other corresponding pairs: < 2 and < 6 < 3 and < 7 < 4 and < 8

14. Parallel lines cut by a transversal 12 34 5 6 78 < 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.

15. Parallel lines cut by a transversal 12 34 5 6 78 Name other alternate interior pairs: < 3 and < 5

16. Parallel lines cut by a transversal 12 34 5 6 78 Name other alternate exterior pairs: < 2 and < 8 < 1 and < 7

17. TRY IT OUT 12 34 5 6 78 The m < 1 is 60 degrees. What is the m<2 ? 120 degrees

18. TRY IT OUT 12 34 5 6 78 The m < 1 is 60 degrees. What is the m<5 ? 60 degrees

19. TRY IT OUT 12 34 5 6 78 The m < 1 is 60 degrees. What is the m<3 ? 60 degrees

20. TRY IT OUT 60120 60 120 60 120 60120

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

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