1. Parallel Lines & Transversals Mrs. Wedgwood Geometry

2. Parallel Lines and Transversals What would you call two lines which do not intersect? _____________ A solid arrow placed on two lines of a diagram indicate the lines are parallel. The symbol ____ is used to indicate parallel lines. AB ___ CD Interior Exterior

3. Parallel Lines and Transversals A slash through the parallel symbol || indicates the lines are not parallel. ________________

4. Transversal A _______, ______, or segment that intersects 2 or more ___________ lines, rays, or segments. Parallel lines transversal Non-Parallel lines transversal Interior Exterior Interior Exterior

5. Parallel Lines and Transversals Transversal - A __________ is a _______ which intersects ____ or _____ lines in a plane. The intersected lines do not have to be parallel. Lines j, k, and m are intersected by line t. Therefore, line t is a ___________ of lines j, k, and m.

6. interior INTERIOR –The space ____________ the 2 lines EXTERIOR -The space __________ the 2 lines exterior

7. Special Angle Relationships ________________ <3 & <6 are ________ Interior angles <4 & <5 are ________ Interior angles <3 & <5 are _____ _____ Interior angles <4 & <6 are _____ _____Interior angles 1 4 2 6 5 78 3 Exterior Angles <1 & <8 are Alternate ________ angles <2 & <7 are _________ Exterior angles <1 & <7 are Same Side _______ angles <2 & <8 are _____ ______ Exterior angles Interior Exterior

8. Special Angle Relationships WHEN THE LINES ARE PARALLEL ♥Alternate Interior Angles are ______________ ♥Alternate Exterior Angles are ________________ ♥Same Side Interior Angles are ________________ ♥Same Side Exterior Angles are _________________ 1 4 2 6 5 78 3 If the lines are not parallel, these angle relationships DO NOT EXIST. Interior Exterior

9. Corresponding Angles & Consecutive Angles Corresponding Angles: Two ________ that occupy ______________ positions. _________, _________, __________, ___________ 12 34 56 78 Interior Exterior

10. Corresponding Angles When two parallel lines are cut by a transversal, pairs of corresponding angles are formed. _____________of corresponding angles are formed. Corresponding pairs of angles are _______________.   Line M B A Line N D E L P Q G F Line L

11. Same Side Interior/Exterior Angles Same Side Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal. Same Side Exterior Angles: Two angles that lie outside parallel lines on the same sides of the transversal. m  3 +m  5 = 180º, m  4 +m  6 = 180º m  1 +m  7 = 180º, m  2 +m  8 = 180º 12 34 56 78 Interior Exterior

12. The angles that lie in the area between the two parallel lines that are cut by a transversal, are called interior angles. A pair of interior angles lie on the ______ ______of the transversal. Interior Angles Line M B A Line N D E L P Q G F Line L 60 0 120 0 60 0   Interior Exterior

13. Alternate Interior/Exterior Angles __________________: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair). ____________________: Two angles that lie outside parallel lines on opposite sides of the transversal. __________________ 12 34 56 78 Interior Exterior

14. Alternate Interior Angles Alternate angles are formed on opposite sides of the transversal and at different intersecting points. Line M B A Line N D E L P Q G F Line L  Pairs of alternate angles are _____________. ___________of alternate angles are formed.

15. Let’s Practice m<1=_________° Find all the remaining angle measures. 1 4 2 6 5 78 3 120

16. Another practice problem Find all the missing angle measures, and name the postulate or theorem that gives us permission to make our statements. 40 120

17. Name the pairs of the following angles formed by a transversal.