1. Objectives: -Define transversal, alternate interior, alternate exterior, same side interior, and corresponding angles -Make conjectures and prove theorems by using postulates and properties of parallel lines and transversals Warm-Up: What weighs more: a pound of feathers or a pound of bricks?

2. Transversal: a line, ray, or segment that intersects two or more coplanar lines, rays, or segments, each at a different point.

3. Interior & Exterior Angles: Interior Exterior

4. Alternate Interior Angles: 12 34 56 78 If two lines cut by a transversal are parallel then, alternate interior angles are congruent. Alternate Interior Theorem:

5. Proof: The Alternate Interior Angles Theorem Given: Prove: StatementsReasons

6. Alternate Exterior Angles: 12 34 56 7 8 Alternate Exterior Angle Theorem: If two lines cut by a transversal are parallel, then alternate exterior angles are congruent.

7. Proof: The Alternate Exterior Angles Theorem Given: Prove: StatementsReasons

8. Same Side Interior Angles: 12 34 56 7 8 If two lines cut by a transversal are parallel, then same side interior angles are supplementary. Same Side Interior Angle Theorem:

9. Proof: The Same Side Interior Angles Theorem Given: Prove: StatementsReasons

10. Corresponding Angles: 12 34 56 7 8 Corresponding Angles Postulate: If two lines cut by a transversal are parallel, then corresponding angles are congruent.

11. Example: 12 34 56 7 8 List all of the angles that are congruent to <1: List all of the angles that are congruent to <2: Identify each of the following: alternate interior angles: alternate exterior angles: same side interior angles: corresponding angles:

12. Example: 12 34 56 7 8 m<4 = m<5 = m<8 = m<2 = m<3 = m<6 = m<7=

13. Example: 12 34 56 7 8 m<1 = m<4 = m<5 = m<8 = m<2 = m<3 = m<6 = m<7 =

14. Example: 12 34 56 7 8 m<1 = m<4 = m<5 = m<8 = m<2 = m<3 = m<6 = m<7 =

15. Example: In triangle KLM, NO is parallel to ML and <KNO is congruent to <KON. Find the indicated measures. m<KNO = m<NOL = m<MNL = m<KON = m<LNO = m<KLN = K NO M L

16. HOMEWORK: page 159-160 #’s 5-12, 22-33