The document discusses relationships between lines and angles formed by transversals. It defines parallel lines as lines that do not intersect and are coplanar, and skew lines as lines that do not intersect and are not coplanar. A transversal is a line that intersects two or more coplanar lines. When a transversal crosses lines, it forms corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles that have specific relationships. Perpendicular lines intersect to form four right angles.

1. 3.1 & 3.2 Lines and Angles Objectives: - Identify relationships between lines - Identify angles formed by transversals

2. Relationships Between Lines Two lines are parallel lines if they are coplanar and do not intersect. Lines that do not intersect and are not coplanar are called skew lines . Two planes that do not intersect are called parallel planes .

3. Relationships Between Lines To write that 2 lines are parallel, you use the symbol: || To show on a drawing that 2 lines are parallel, you add arrows:

4. Parallel Postulate If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line. P

5. Perpendicular Postulate If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line. P

6. Transversals A transversal is a line that intersects two or more coplanar lines at different points. t 1 2 3 4 5 8 6 7

7. Transversals Two angles are corresponding angles if they occupy corresponding positions. t 1 2 3 4 5 8 6 7

8. Transversals Two angles are alternate exterior angles if they lie outside the two lines on opposite sides of the transversal. t 1 2 3 4 5 8 6 7

9. Transversals Two angles are alternate interior angles if they lie between the two lines on opposite sides of the transversal. t 1 2 3 4 5 8 6 7

10. Transversals Two angles are consecutive interior angles if they lie between the two lines on the same side of the transversal. t 1 2 3 4 5 8 6 7 Also called same side interior angles .

11. Transversals List all the sets of corresponding angles: 1&5, 2&6, 3&7, 4&8 t 1 2 3 4 5 8 6 7

12. Transversals List all the sets of alternate interior angles: 3&6, 4&5 t 1 2 3 4 5 8 6 7

13. Transversals List all the sets of alternate exterior angles: 1&8, 2&7 t 1 2 3 4 5 8 6 7

14. Transversals List all the sets of consecutive interior angles: 3&5, 4&6 t 1 2 3 4 5 8 6 7

15. Look at the Chinese food pictures on page 132 Which chopsticks are parallel? Which chopsticks are skew? Which chopsticks are intersecting?

16. Perpendicular Theorems If 2 lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.

17. Perpendicular Theorems If 2 sides of 2 adjacent acute angles are perpendicular, then the angles are complementary.

18. Perpendicular Theorems If 2 lines are perpendicular, then they intersect to form 4 right angles.

19. Homework Worksheets