Angles and Parallel Lines

1. Angles and Parallel Lines

2. Congruent Complements Theorem If ∠4 and ∠5 are complementary and ∠5 and ∠6 are complementary Then ∠4 ∠6

3. Congruent Supplements Theorem • If ∠1 and ∠2 are supplementary and ∠2 and ∠3 are supplementary Then ∠1 ∠3

4. 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

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 1 2 3 4 5 6 7 8

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 1 2 3 4 5 6 7 8

7. 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 1 2 3 4 5 6 7 8

8. 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 1 2 3 4 5 6 7 8