Points, Lines, & Planes

1. Points, Lines, & Planes Section 1-1

2. Undefined Terms in Geometry There are 5 undefined terms in geometry that have no formal definition, but that we have developed a common notion about. point line plane between congruent

3. 3 Parts to a Good Definition • Identifies the word or phrase as a member of a set of words or phrases • Shows how the word or phrase can be distinguished from other members of the set • Is always reversible.

4. Example: Define a pen. “A pen is an instrument used for writing”. (Is this a good defn.?) No. There are other members of the set of instruments used for writing. How can you distinguish the pen from other members of this set? A pen uses ink. “A pen is a writing instrument which uses ink.”

5. Define the following terms. • pencil • ruler • dog

6. Point – All geometric figures contain points. They have no size. In a figure, a point is represented by a dot. Points are named by capital letters.

7. Plane - Planes can be thought of as flat surfaces that extend indefinitely in all directions and have no thickness. A plane is often represented by a parallelogram. They are usually named by a capital letter or by 3 noncollinear points on the plane.

8. Line – Lines extend indefinitely and have no thickness or width. In a figure, a line is shown with arrows at each end. Lines are usually named by lower case script letters or by writing capital letters for 2 points on the line, with a double arrow over the pair of letters.

9. Space – a boundless, 3-dimensional set of all points. Collinear– points that lie on the same line Coplanar- points that lie on the same plane

10. 2 points determine a line. 3 noncollinear points determine a plane. The intersection of 2 figures is the set of points that are in both figures

11. 2 lines intersect at a point. 2 planes intersect in a line.

12. A line and a plane intersect at a point.