Points, Lines, & Planes

1. Points, Lines, & Planes

2. The 3 Undefined Terms in Geometry Point Represents location Has no size Line Straight arrangement of many points Has length but no width Plane Flat surface that continues forever Has length and width but no thickness ●

3. Naming points To name a point, use a capital letter. • • • points A, B, and C

4. Naming lines To name a line, use a lower case letter OR any two points on the line. • • line m or line AB or line BA

5. Naming planes To name a plane, use a capital letter in the corner of the plane OR use 3 noncollinear points on the plane. • • • plane R, or plane ABC, CBA, BAC, or any combination of the 3 points

6. Terms to Know • Collinear points points that lie on the same line (A, B, & C are collinear points) • Coplanar points points that lie on the same plane (A, B, & C are coplanar points) • • • • • •

7. Terms to Know • Intersecting lines lines that share at least one point • lines j and k intersect at point X

8. Terms to Know • Parallel lines lines that lie in the same plane that do not intersect lines j and k are parallel

9. Terms to Know • Skew lines lines that are not in the same plane that do not intersect and are not parallel j k lines j and k are skew

10. Relationships between2 different lines Parallel (no points in common)

11. Relationships between2 different lines Intersect (one point in common) lines k and j intersect at point X •

12. Relationships between2 different lines Skew (no points in common)

13. Relationships between 2 different planes Parallel (no points in common)

14. Relationships between 2 different planes Intersect (intersect to form a line)

15. Relationships betweena line and a plane When a linelies on a plane, the intersection is a line.

16. Relationships betweena line and a plane When a line is parallel to a plane, there is no intersection. When a lineintersects a plane, the intersection is a point.

17. Checking your understanding • What are the 3 undefined terms in geometry? • _______ points lie on the same plane. • _______ lines lie in different planes and do not intersect. • The intersection of 2 planes is a _______. • The intersection of 2 lines is a _______. • The intersection of a line and plane is a_______. • If 2 lines have no points in common, then they are _______. • What possible relationships exist when 3 planes intersect?

18. How well did you do? • Point, line, and plane • Coplanar points • Skew lines • Line • Point • Point • Parallel • They will intersect to form a line or a point.