1. Properties of Parallel Lines

2.  Transversal: line that intersects two coplanar lines at two distinct points Transversal

3. Properties of Parallel Lines The pairs of angles formed have special names… Transversal 5 6 1 3 42 7 8 l m t

4. Alternate Interior Angles <1 and <2 <3 and <4 5 6 1 3 42 7 8 l m t

5. Same-side Interior Angles <1 and <4 <2 and <3 5 6 1 3 42 7 8 l m t

6. Corresponding Angles <1 and <7 <2 and <6 <3 and <8 <4 and <5 5 6 1 3 42 7 8 l m t

7. Properties of Parallel Lines Postulate 3-1Corresponding Angles Postulate If a transversal intersects two parallel lines, then corresponding angles are congruent t l m line l || line m 1 2 m<1 =m <2

8. Properties of Parallel Lines Theorem 3-1Alternate Interior Angles Theorem If a transversal intersects two parallel lines, then alternate interior angles are congruent. t l m line l || line m 1 2 m<2 = m<3 3

9. Properties of Parallel Lines Theorem 3-2Same-Side Interior Angles Theorem If a transversal intersects two parallel lines, then same-side interior angles are supplementary. t l m line l || line m 1 2 m<1 + m<2 = 180 3

10. Two-Column Proof Given: a || b Prove: m<1 = m<3 StatementsReasons a b t 3 4 1 1. a || b 1. Given 2.2. Corr. Angle Postulate 3.3. Vert. Angles 4.4. Set Statement 1 = Statement 2 * This proves why alternate interior angles are congruent *

11. Two-Column Proof Given: a || b Prove: <1 and <2 are supplementary StatementsReasons a b t 2 3 1 1. a || b 1. Given 2.2. Corr. Angle Postulate 3.3. Consecutive Angles

12. Finding Angle Measures <1 <2 <3 <4 <5 <6 <7 <8 a b c d a || bc || d 876 2 50° 5 1 3 4

13. Using Algebra to Find Angle Measures Find the value of x and y. x = y = ▲ ▲ x 50° y70° 2xy (y – 50) ▲ ▲