6.3 Parallel Plane Facts

1. 6.3 Parallel Plane Facts • Objectives: • Recognize lines parallel to planes, parallel lines and skew lines • Use properties relating parallel planes and lines

2. Definition: If a line and a plane are parallel, then they do not intersect. A B m

3. Definition: If 2 planes are parallel, then they do not intersect. m n

4. Definition: If 2 planes are parallel, then they do not intersect. m n

5. Definition: If 2 planes are parallel, then they do not intersect. m n

6. Definition: If 2 lines are skew, they are not coplanar. m n

7. Definition: If 2 lines are skew, they are not coplanar. m n

8. Theorem 49: If a plane intersects two parallel planes, then the lines of intersection are parallel. B n A m D C

9. Theorem 49: If a plane intersects two parallel planes, then the lines of intersection are parallel. B n A m D C

10. Theorem 49: If a plane intersects two parallel planes, then the lines of intersection are parallel. B n A m D C

11. Parallel Properties of Lines and Planes In a plane if two lines are perpendicular to the same line, then they are parallel. If a line is perpendicular to one of two parallel planes, then it is perpendicular to the other plane as well. If two planes are parallel to the same plane, then they are parallel to each other. If two lines are perpendicular to the same plane, then they are parallel to each other. If a plane is perpendicular to one of two parallel lines, then it is perpendicular to the other line as well. Parallel Properties of Lines and Planes In a plane if two lines are perpendicular to the same line, then they are parallel. If a line is perpendicular to one of two parallel planes, then it is perpendicular to the other plane as well. If two planes are parallel to the same plane, then they are parallel to each other. If two lines are perpendicular to the same plane, then they are parallel to each other. If a plane is perpendicular to one of two parallel lines, then it is perpendicular to the other line as well.