Parallel Lines with Transversals
- 1. Parallel Lines and Transversals
- 2. Parallel Lines and Transversals 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 2. < 2 and < 10 are alternate interior angles. Identifying Angles – Check for Understanding 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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 .
- 11. Parallel Lines and Transversals 2. < 2 and < 10 are alternate interior angles. Identifying Angles – Check for Understanding 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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.
- 12. Parallel Lines and Transversals 4. < 1 and < 15 are alternate exterior angles. <3 and < 5 are alternate interior angles. Identifying Angles – Check for Understanding 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Determine if the statement is true or false. If false, correct the statement.
- 13. Parallel Lines and Transversals 4. < 1 and < 15 are alternate exterior angles. 3. < 3 and < 5 are alternate interior angles. Identifying Angles – Check for Understanding 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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.
- 14. Parallel Lines and Transversals 6. < 10 and < 11 are consecutive interior angles. 5. < 6 and < 12 are alternate interior angles. Identifying Angles – Check for Understanding 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Determine if the statement is true or false. If false, correct the statement.
- 15. Parallel Lines and Transversals 6. < 10 and < 11 are consecutive interior angles. 5. < 6 and < 12 are alternate interior angles. Identifying Angles – Check for Understanding 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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 .
- 16. Parallel Lines and Transversals 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. Identifying Angles – Check for Understanding 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
- 17. Parallel Lines and Transversals 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. Identifying Angles – Check for Understanding 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 False– The angles are adjacent angles on transversal r . True – The angles are corresponding angles on transversal s .