1. Warm-up

2. Agenda  Begin Chapter 3  Homework  Bring your book on Tuesday

3. Chapter 3 Goal Understanding Perpendicular and Parallel Lines/Planes

4. Parallel Lines A definition for Parallel Lines - two lines in the same plane are parallel if and only if they never meet. In geometry, the symbol || means "parallel to". For example in the diagram we would write ||.

5. Parallel Planes Parallel Planes:Planes Intersecting Plane ABC: plane ADR || plane BCSplane ABT intersects plane ABC at plane RSC || plane ABTplane ADR intersects plane ABC at plane RST || plane ADCplane BCS intersects plane ABC at

6. SKEW LINES - Two lines are skew if they do not intersect and are not in the same plane. Skew Lines and Parallel Lines and Skew Lines and Intersecting (All lie in plane BAD) and Line Type:Two Lines

7. Transversals Often in geometry lines intersect or cross one another. A line that intersect TWO OR MORE lines in a plane at different points is called a TRANSVERSAL. When a transversal intersects with two other lines, it forms eight angles with these lines. Each of these angles has a specific name and important relationships to each other.

8. Transversal Line Mini-project Using lined paper and a ruler 1) Draw two parallel lines 2) Draw a third line so that it intersects the || lines diagonally. 3) Number the angles 1 - 8 4) Measure each angle using a protractor 1 2 34 56 7 8

9. Postulate 3-1 Corresponding Angles If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.  1 and  5  2 and  6  3 and  7  4 and  8

10. Theorem 3-1 Alternate Interior If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.  3 and  6  4 and  5

11. Theorem 3-2 Consecutive Interior Angle If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary.  3 and  5  4 and  6

12. Theorem 3-3 Alternate Exterior Angle If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent.  1 and  8  2 and  7

13. Theorem 3-4 Perpendicular Transversal In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.

14. Answers Ahead

15. 3-1 Study Guide

17. 3-2 Angles and Parallel Lines

19. 16 pairs

20. 3-2 Angles and Parallel Lines

21. Caution – Answers Ahead

22. 3-2 Study Guide

25. Homework  3-1 Practice  3-2 Practice