1. 1-2: Points, Lines, and Planes

2. Undefined Terms In geometry, some words are undefined.
Undefined terms are the basic ideas that you can use to build the definitions of all other figures in geometry.
A point indicates a location and has no size.
Usually represented by a dot and named with a capital letter.

3. Undefined Terms, con’t
A line is a straight path that extends in two opposite directions without end.
Usually represent by a straight line with arrow heads on each end and named by one lowercase letter or two capital letters, such as
A plane is represented by a flat surface that extends without end in all directions.
Usually represented by a quadrilateral and named by one capital letter or three points that lie on it.

4. Collinear and Coplanar
Points that lie on the same line are collinear points.
Points and lines that lie in the same plane are coplanar.
All the points of a line are coplanar!

5. Naming Points, Lines and Planes
What are two other ways to name ?
What are two other ways to name plane P?
What are the names of three collinear points?
What are the names of four coplanar points?

6. Defined Terms
A segment is part of a line that consists of two endpoints and all points between them.
Segments are named by their endpoints.
A ray is part of a line that consists of one endpoint and continues in the other direction.
Rays are named by their endpoint and another point on the ray (the order of the points indicates the direction of the ray!).

7. Defined Terms, con’t
Opposite rays are two rays that share the same endpoint and form a line.
How would you name the opposite rays above?

8. Naming Segments and Rays
What are the names of the segments in the figure?
What are the names of the rays?
Which of the rays are opposite rays?

9. Postulates A postulate is an accepted statement of fact.
Postulates cannot be proven!
Postulate 1-1 : Through any two points there is exactly one line.

10. Intersection
When you have two or more figures, their intersection is the set of points the figures have in common.
Postulate 1-2: If two distinct lines intersect, then they intersect in exactly one point.
Postulate 1-3: If two distinct planes intersection, then they intersect in exactly one line.

11. Finding the Intersection of Two Planes
Each surface of the box below represents part of a plane.
What is the intersection of plane ADC and plane BFG?
*NOTE: When naming a plane, list corner points in consecutive order!

12.  What is the intersection of plane AEH and plane EGH?

13. Noncollinear Points
Points which do not lie on the same line are noncollinear.
Three or more points are noncollinear if they are not ALL on the same line!
Postulate 1-4: Through any three noncollinear points there is exactly one plane.

14. Using Postulate 1-4
What plane contains points N, P, and Q? Shade the plane.
What plane contains points J, M, and Q? Shade the plane.