3.  Transversal: a line that intersects two coplanar lines at two different points. T (transversal) n m 1 5 6 3 4 7 2 8

4.  The angles formed by a transversal have special properties. Alternate interior angles T n m 1 3 4 2 ∠1 and ∠2 are alt. int. angles ∠3 and ∠4 are alt. int. angles

5.  Same-side interior angles T n m 1 3 4 2 ∠1 and ∠4 are same- side int. ∠3 and ∠2 are same- side int.

6.  Corresponding Angles T n m 1 5 6 3 4 7 2 8 ∠2 and ∠6 are corresponding ∠1 and ∠7 are corresponding ∠4 and ∠5 are corresponding ∠3 and ∠8 are corresponding

7. 1. Name a pair of alt. int. angles 2. Name a pair of same-side int. 3. Name 2 pairs of corresponding. T (transversal) n m 3 1 2 4 5 7 6 8

8.  Corresponding Angles Postulate (3-1) ◦ If a transversal intersects two parallel lines, then corresponding angles are congruent. ∠1 ≅ ∠2

9. Alternate Interior Angles Theorem (3-1) ◦ If a transversal intersects two parallel lines, then alternate interior angles are congruent. Same Side Interior Angles Theorem (3-2) o If a transversal intersects two parallel lines, then same-side interior angles are supplementary. ∠1 ≅ ∠3 m∠1 + m∠2 = 180 1 23

10. Given: a ‖ b  what you know (either from a picture or statement) Prove: ∠1 ≅ ∠2  what you must show Statements Reasons 1. 2. 3. 4. 1. 2. 3. 4.

11.  Prove theorem 3-2 (If a transversal intersects two parallel lines, then same-side interior angles are supplementary.)  Given:  Prove: ∠1 and ∠2 are supplementary 1 23

12.  ∠6 = 50°  Find the measures of the missing angles

13.  Find the value of x and y x° y° 50° 70°

14.  Find the values of x and y, then find the measure of the angles. 2x° y° (y-50)°

15.  Pg 119-120 1-7, 10, 11-16, 17, 23