Points, Lines, & Planes Section 1-1

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 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.

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.”

Define the following terms. pencil ruler dog

Point – All geometric figures contain points. They have no size 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.

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.

Line – Lines extend indefinitely and have no thickness or width 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.

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

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

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

A line and a plane intersect at a point.