1. Parallel Lines and Transversals. Angles and parallel lines. Lesson Objective Explore relationships of the angles formed by a transversal cutting parallel lines. Vocabulary Parallel lines, parallel planes, transversal, consecutive interior angels, alternative exterior angels, alternative interior angels, corresponding angels.  Video

2. Parallel Lines: Coplanar lines that do not intersect. s c d l w x  l x

3. Example 1-1c Name all segments that are parallel to Answer: A B C E F G H D

4. Example 1-1e Use the figure to name each of the following. Answer: plane XYZ Answer:

5. Transversal: A line that intersects two or more lines in a plane at different points. Transversal crossing two lines This transversal crosses two parallel lines This transversal cut across three lines 

6. Transversal and angles m transversal k 2 1 43 7 6 5 8 NAMEANGLES Exterior angles Interior angles Consecutive interior angles Alternate exterior angles Alternate interior angles Corresponding angles  11 33 22 77 88 44 66 55 66 33 44 55 11 22 77 88 33 55 44 66 11 55 22 66 33 77 44 88 mk

7. Corresponding Angles Postulate If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.  m k 2 1 43 7 6 5 8 mk 11 33 22 44 66 55 77 88    

8. When two parallel lines are cut by a transversal, then…. transversal ….each pair of alternative interior angles is congruent. 2 1 43 7 6 5 8 33 66  44 55  ….each pair of alternative exterior angles is congruent. 11 22 77 88  ….each pair of consecutive interior angles is supplementary. m4+m4+m  6=180 m  3+m  5=180  geogebra

9. Answer: Example 2-1a Corresponding Angles Postulate Vertical Angles Theorem Transitive Property Definition of congruent angles Substitution In the figure and Find

10. Example 2-1b Answer : In the figure and Find

11. Example 2-2a Grid-In Test Item What is the measure of  RTV? Read the Test Item Be sure to identify it correctly on the figure. Use an auxiliary line.

12. Example 2-2b Solve the Test Item Alternate Interior Angles Theorem Definition of congruent angles Substitution

13. Example 2-2c Angle Addition Postulate Write each digit of 125 in a column of the grid. Then shade in the corresponding bubble in each column. Definition of congruent angles Substitution Alternate Interior Angles Theorem

14. Example 2-2c Answer:

15. Example 2-2d Grid-In Test Item What is the measure of  IGE? Answer: J K

16. Example 2-3e Ifandfind x and y. Find x. by the Corresponding Angles Postulate. ALGEBRA

17. Example 2-3f Definition of congruent angles Substitution Subtract x from each side and add 10 to each side. Definition of congruent angles Substitution Find y. by the Alternate Exterior Angles Theorem.

18. Example 2-3g Simplify. Add 100 to each side. Divide each side by 4. Answer:

19. Example 2-3h Answer: ALGEBRAIf andfind x and y.