1. 1 Angles and Parallel Lines

2. 2 Transversal Definition: A line that intersects two or more lines in a plane at different points is called a transversal. When a transversal t intersects line n and m, eight angles of the following types are formed: Exterior angles Interior angles Consecutive angles Alternate angles t m n

3. 3 Vertical Angles & Linear Pair Vertical Angles: Linear Pair:  1   4,  2   3,  5   8,  6   7 Two angles that are opposite angles. Vertical angles are congruent.  1 &  2,  2 &  4,  4 &  3,  3 &  1,  5 &  6,  6 &  8,  8 &  7,  7 &  5 Supplementary angles that form a line (sum = 180  ) 12 34 56 78

4. 4 Angles and Parallel Lines If two parallel lines are cut by a transversal, then the following pairs of angles are congruent. 1. Corresponding angles 2. Alternate interior angles 3. Alternate exterior angles If two parallel lines are cut by a transversal, then the following pairs of angles are supplementary. 1. Consecutive interior angles 2. Consecutive exterior angles Continued…..

5. 5 Corresponding Angles Corresponding Angles: Two angles that occupy corresponding positions. Corresponding Angles Postulate: If two parallel lines are cut by a transversal, then the Corresponding angles are congruent.  2   6,  1   5,  3   7,  4   8 12 34 56 78

6. 6 Same Side or Consecutive Angles Consecutive Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal. Consecutive Interior Angles Theorem: If two parallel lines are cut by a transversal, then the Consecutive Interior Angles are supplementary. m  3 +m  5 = 180º, m  4 +m  6 = 180º 12 34 56 78

7. 7 Same Side or Consecutive Angles Consecutive Exterior Angles: Two angles that lie outside parallel lines on the same sides of the transversal. Consecutive Exterior Angles Theorem: If two parallel lines are cut by a transversal, then the Consecutive Exterior Angles are supplementary. m  1 +m  7 = 180º, m  2 +m  8 = 180º 12 34 56 78

8. 8 Alternate Angles Alternate Interior Angles: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair). Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, then the Alternate Interior Angles are congruent.  3   6,  4   5 12 34 56 78

9. 9 Alternate Angles Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal. Alternate Exterior Angles Theorem: If two parallel lines are cut by a transversal, then the Alternate Exterior Angles are congruent.  2   7,  1   8 12 34 56 78

10. Example 1 Find all numbered angles Angles and Parallel Lines 10 60° 1 2 34

11. Example 2 Find x and y Angles and Parallel Lines 11 AB C D 30  5y  2x  (x-y) 