1. 3.2: Properties of Parallel Lines 1

2. Today’s Objectives  Understand theorems about parallel lines  Use properties of parallel lines to find angle measurements

3. Corresponding Angles Postulate  Postulate 3-1: If a transversal intersects two parallel lines, then corresponding angles are congruent 12 34 56 78 Indicates Parallel

4. Alternate Interior Angles Theorem  Theorem 3-1: if a transversal intersects two parallel lines, then alternate interior angles are congruent 12 34 56 78

5. Consecutive Interior Angles Theorem  Theorem 3-2: if a transversal intersects two parallel lines, then consecutive (same-side) interior angles are supplementary 12 34 56 78

6. Alternate Exterior Angles Theorem  Theorem 3-3: if a transversal intersects two parallel lines, then alternate exterior angles are congruent 12 34 56 78

7. 7 Angles and Parallel Lines If two parallel lines are cut by a transversal, then the following pairs of angles are CONGRUENT.  Corresponding angles  Alternate interior angles  Alternate exterior angles If two parallel lines are cut by a transversal, then the following pairs of angles are SUPPLEMENTARY.  Consecutive interior angles  Consecutive exterior angles

8. Example  Fill in all of the angle measurements if m<2 = 68. 12 34 56 78

9. Example

10.  Solve for x. 17(8) + 14=150 4(8) – 2 =30

11. Take Home  Special angles have special relationships  Alternate  Congruent  Consecutive (Same-Side)  Supplementary  Corresponding  Congruent