1. Parallel Lines Advanced Geometry Parallel and Perpendicular Lines Lesson 1

2. Lines (segments & rays, also) are either intersecting, or skew. parallel,

3. and are skew. do not intersect Skew Lines are not coplanar

4. Planes can be parallel OR intersecting.

5. Name all segments that are parallel to. Name all segments that are skew to. Name all segments that intersect. Example : Name all planes that are parallel to plane DEF. Figure from p. 143.

6. Transversal Identify the pairs of lines to which each given line is a transversal. m p l and n; l and p; n and p l and m; l and n; m and n

7. Whenever there are two lines and a transversal, eight angles are formed. interior angles – angles between the two lines exterior angles – angles outside the two lines ∠ 3, ∠ 4, ∠ 5, ∠ 6 ∠ 1, ∠ 2, ∠ 7, ∠ 8 a b t

8. Alternate Interior Angles different sides of the transversal AIA both angles are interior different sides of the transversal Alternate Exterior Angles AEA both angles are exterior ∠ 3 and ∠ 6 ∠ 4 and ∠ 5 ∠ 1 and ∠ 8 ∠ 2 and ∠ 7 a b t Alternate Interior Angles Alternate Exterior Angles Alternate Exterior Angles

9. Consecutive Interior Angles same side of the transversal CIA both angles are interior same side of the transversal Corresponding Angles one interior angle and one exterior angle ∠ 3 and ∠ 5 ∠ 4 and ∠ 6 ∠ 1 and ∠ 5 ∠ 2 and ∠ 6 ∠ 3 and ∠ 7 ∠ 4 and ∠ 8 a b t Consecutive Interior Angles

10. Identify each pair of angles and AIA, AEA, CIA, corresponding angles, vertical angles, or a linear pair. ∠ 5 and ∠ 12 ∠ 10 and ∠ 3 ∠ 4 and ∠ 7 ∠ 10 and ∠ 11 ∠ 2 and ∠ 12 ∠ 3 and ∠ 14 AEA corresponding angles vertical angles CIA linear pair AIA

11. Name the transversal that forms each pair of angles. Then identify the pair of angles. ∠ 8 and ∠ 6 ∠ 10 and ∠ 14 ∠ 2 and ∠ 1 6 ∠ 10 and ∠ 11 corresponding angles AIA AEA CIA a b c b

12. When the lines cut by a transversal are parallel, the four angle pairs have a special relationship. AIA are congruent. AEA are congruent. CIA are supplementary. Corresponding angles are congruent. Reminder: Vertical angles are ALWAYS congruent. Linear pairs are ALWAYS supplementary.

13. In the figure a || b and m ∠ 4 = 51. Find the measures of all numbered angles. Justify each answer. a b

14. Find the measure of each angle if m ∠ 1 = 62 and m ∠ 7 = 107.

15. What is the measure of ∠ RTV?

16. If m ∠ 2 = 4x + 7 and m ∠ 3 = 5x – 13, find m ∠ 3.

17. If m ∠ 5 = 2x – 10, m ∠ 6 = 4(y – 25), and m ∠ 7 = x + 15. find x and y.