1. Parallel Lines and Transversals

2. What would you call two lines which do not intersect? Parallel A solid arrow placed on two lines of a diagram indicate the lines are parallel. The symbol || is used to indicate parallel lines. AB || CD

3. Parallel Lines and Transversals A slash through the parallel symbol || indicates the lines are not parallel. AB || CD

4. Parallel Lines and Transversals Transversal - A transversal is a line which intersects two or more lines in a plane. The intersected lines do not have to be parallel. Lines j, k, and m are intersected by line t. Therefore, line t is a transversal of lines j, k, and m.

5. Parallel Lines and Transversals Identifying Angles - 1 2 3 4 5 6 7 8 Exterior angles are on the exterior of the two lines cut by the transversal. The exterior angles are: <1, <7, <2, <8

6. Parallel Lines and Transversals Identifying Angles - 1 2 3 4 5 6 7 8 Interior angles are on the interior of the two lines cut by the transversal. The interior angles are: <3, <5, <4, <6

7. Parallel Lines and Transversals Identifying Angles - 1 2 3 4 5 6 7 8 Alternate interior angles are on the interior of the two lines and on opposite sides of the transversal. Alternate interior angles are: <3 & <6, <4 & <5

8. Parallel Lines and Transversals Identifying Angles - 1 2 3 4 5 6 7 8 Alternate exterior angles are on the exterior of the two lines and on opposite sides of the transversal. Alternate exterior angles are: <1 & <8, <2 & <7

9. Parallel Lines and Transversals Identifying Angles - 1 2 3 4 5 6 7 8 Corresponding angles are on the corresponding side of the two lines and on the same side of the transversal. Corresponding angles are: <1 & <5, <3 & <7, <2 & <6, <4 & <8

10. Parallel Lines and Transversals Identifying Angles - 1 2 3 4 5 6 7 8 Vertical are on the opposite side of the two lines and on the opposite side of the transversal. Vertical angles are: <1 & <4, <3 & <2, <5 & <8, <6 & <7

11. 2. < 2 and < 10 are alternate interior angles. Parallel Lines and Transversals Identifying Angles – Check for Understanding 1 2 3 4 5 6 78 9 10 1112 1314 15 16 Determine if the statement is true or false. If false, correct the statement. 1.Line r is a transversal of lines p and q.

12. 2. < 2 and < 10 are alternate interior angles. Parallel Lines and Transversals Identifying Angles – Check for Understanding 1 2 3 4 5 6 78 9 10 1112 1314 15 16 Determine if the statement is true or false. If false, correct the statement. 1.Line r is a transversal of lines p and q. True – Line r intersects both lines in a plane. False - The angles are corresponding angles on transversal p.

13. 4. < 1 and < 15 are alternate exterior angles. 3.<3 and < 5 are alternate interior angles. Parallel Lines and Transversals Identifying Angles – Check for Understanding 1 2 3 4 5 6 78 9 10 1112 1314 15 16 Determine if the statement is true or false. If false, correct the statement.

14. 4. < 1 and < 15 are alternate exterior angles. 3. < 3 and < 5 are alternate interior angles. Parallel Lines and Transversals Identifying Angles – Check for Understanding 1 2 3 4 5 6 78 9 10 1112 1314 15 16 Determine if the statement is true or false. If false, correct the statement. False – The angles are vertical angles created by the intersection of q and r. True - The angles are alternate exterior angles on transversal p.

15. 6. 10 and 11 are vertical angles. 5. < 6 and < 12 are alternate interior angles. Parallel Lines and Transversals Identifying Angles – Check for Understanding 1 2 3 4 5 6 78 9 10 1112 1314 15 16 Determine if the statement is true or false. If false, correct the statement.

16. 6. 10 and 13 are vertical angles. 5. < 6 and < 12 are alternate interior angles. Parallel Lines and Transversals Identifying Angles – Check for Understanding 1 2 3 4 5 6 78 9 10 1112 1314 15 16 Determine if the statement is true or false. If false, correct the statement. True – The angles are alternate interior angles on transversal q. True – The angles are consecutive interior angles on transversal s.

17. Determine if the statement is true or false. If false, correct the statement. 7. < 3 and < 4 are alternate exterior angles. 8. 16 and 14 are correxponding angles. Parallel Lines and Transversals Identifying Angles – Check for Understanding 1 2 3 4 5 6 78 9 10 1112 1314 15 16

18. Determine if the statement is true or false. If false, correct the statement. 7. < 3 and < 4 are alternate exterior angles. 8. < 16 and < 14 are corresponding angles. Parallel Lines and Transversals Identifying Angles – Check for Understanding 1 2 3 4 5 6 78 9 10 1112 1314 15 16 False– The angles are adjacent angles on transversal r. True – The angles are corresponding angles on transversal s.