1. Parallel Lines and Transversals Geometry D – Section 3.1

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 - When two parallel lines are cut by another line this is called a transversal. Parallel lines t and s are intersected by line j, k and m. Therefore, line j, k and m are a transversal of lines t and s. S

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:

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:

7. Parallel Lines and Transversals Identifying Angles - Vertical angles are: When two lines intersect they form two pairs of “opposite” angles called vertical angles. < 1 and < 3 < 2 and < 4 Vertical angles are congruent. Congruent means angles with the same measurement.

8. Parallel Lines and Transversals Identifying Angles - If the sum of the measures of two angles is 90° the angles are complementary. Angles a and b are complementary. If the sum of the measures of two angles is 180°, they are supplementary. Angles a and b are supplementary.

9. 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: Alternate interior angles are congruent.

10. 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: Alternate exterior angles are congruent.

11. 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: Corresponding angles are congruent.

12. http://www.mrperezonlinemathtutor. com/G/1_2_Angles_in_Parallel_lin es.html

13. 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.

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 15 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. False- 10 and 16 are vertical angles

16. 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 a linear pair, they are supplementary angles. True – The angles are corresponding on transversal s.

17. http://www.mathopenref.com/angle salternateinterior.html