1. 1.2 Points, Lines and Planes
Geometry

2. Objectives/Assignment:
Understand and use the basic undefined terms and defined terms of geometry.
Sketch the intersections of lines and planes.

3. Using Undefined terms and definition
A definition uses known words to describe a new word. In geometry, some words such as point, line and plane are undefined terms or not formally defined.

4. Using Undefined terms and definition
A point is a location.
A point has no shape or size.
It is usually represented by a small dot.
Always use a CAPITAL LETTER to name a point. A
Point A

5. Using Undefined terms and definitionl
A line is made up of points.
A line has no thickness or width.
A line extends in one dimension.
It is usually represented by a straight line with two arrowheads to indicate that the line extends without end in two directions.
Name a line by any TWO points on the line, or a lowercase script letter. A B
Line l or AB

6. A few basic concepts . . .
Must be commonly understood without being defined. One such concept is the idea that a point lies on a line or a plane.
Collinear points are points that lie on the same line. (Points P, Q, and R)
Coplanar points are points that lie on the same plane. (Points X, Y, and Z)

7. Using Undefined terms and definition
A plane is a flat surface made up of points.
A plane extends indefinitely in all directions.
It is usually represented by a shape that looks like a tabletop or wall.
You must imagine that the plane extends without end even though the drawing of a plane appears to have edges.
A plane is named by any THREE non-collinear points on the plane, or an uppercase script letter. A B C Q
Plane Q or plane ABC

8. Ex. 1: Naming Collinear and Coplanar PointsH
Name three points that are collinear
Solution:
D, E and F lie on the same line, so they are collinear. G E F D

9. Ex. 2: Naming Collinear and Coplanar PointsH
Name four points that are coplanar.
Solution:
D, E, F, and G lie on the same plane, so they are coplanar. Also D, E, F, and H are coplanar; although, the plane containing them is not drawn. G E F D

10. Ex. 3: Naming Collinear and Coplanar PointsH
Name three points that are not collinear.
Solution:
There are many correct answers. For instance, points H, E, and G do not lie on the same line. G E F D

11. Definition:
A ray is a portion of a line that extends indefinitely in one direction.
A ray begins at an initial point.
A ray is names by TWO points.
NOTE that is not the same as !!! These rays have different initial points.

12. Definition:
Opposite rays are two rays with a common initial point that extend to form a line.
and are opposite rays.
Opposite rays are collinear.
NOTE and are NOT opposite rays. They do not form a line!!!

13. More . . . l
Another undefined concept in geometry is the idea that a point on a line is between two other points on the line. You can use this idea to define other important terms in geometry.
Consider the line AB (symbolized by AB). B A
Line l or AB

14. A B
More . . .
Segment AB l
The line segment or segment AB (symbolized by AB) consists of the endpoints A and B, and all points on AB that are between A and B. B A
Line l or AB

15. A B
More . . .
Ray AB l
The ray AB consists of the initial point A and all points on AB that lie on the same side of A as point B. B A
Line l or AB

16. More . . .
If C is between A and B, then CA and CB are opposite rays.
Like points, segments and rays are collinear if they lie on the same line. So, any two opposite rays are collinear. Segments, rays and lines are coplanar if they lie on the same plane. l B C A
Line l or AB