Properties of Parallel Lines

1. Properties of Parallel Lines

2. Properties of Parallel Lines • 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… t Transversal 5 6 1 3 l 4 2 m 8 7

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

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

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

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

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

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

10. Two-Column Proof t Given: a|| b Prove: m<1 = m<3 Statements Reasons 4 a 3 1 b 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 t Given: a|| b Prove: <1 and <2 are supplementary Statements Reasons 3 a 2 1 b 1. a|| b 1. Given 2. 2. Corr. Angle Postulate 3. 3. Consecutive Angles

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

13. Using Algebra to Find Angle Measures Find the value of x and y. x = y = ▲ ▲ 50° y 70° x ▲ 2x y (y – 50) ▲