Grade 9 Basic Concepts in Geometry

Point: A point is a location in space. It has no size or dimension. It is usually represented by a dot and named with a capital letter (e.g., Point A).

Line: A line is a straight path that extends infinitely in both directions. It has no thickness. A line can be named by a single lowercase letter (e.g., line l) or by two points on the line (e.g., line AB).

Plane: A plane is a flat surface that extends infinitely in all directions. It has no thickness. A plane can be named by a single capital letter (e.g., Plane P) or by three non-collinear points in the plane.

Undefined Terms: Point, Line, and Plane are considered undefined terms in geometry because they are fundamental and described rather than formally defined.

Collinear Points: Three or more points that lie on the same straight line are called collinear points.
Example: Points A, B, and C are collinear if they all lie on the same line.

Non-collinear Points: Three or more points that do not lie on the same straight line are called non-collinear points.
Example: Points P, Q, and R are non-collinear if no single line can pass through all three points.

Important Note: Any two distinct points are always collinear, as a unique straight line can always be drawn through any two points. The concept of collinearity is relevant for three or more points.

Intersecting Lines: Two distinct lines in a plane that cross each other at exactly one point are called intersecting lines. The point where they cross is called the point of intersection.
Example: Two roads crossing each other form intersecting lines.

Parallel Lines: Two distinct lines in a plane that never intersect, no matter how far they are extended, are called parallel lines. They maintain a constant distance from each other.
Example: Opposite edges of a ruler, railway tracks.

In a Plane: These definitions apply to lines lying in the same plane. Lines that are not in the same plane and do not intersect are called skew lines (a concept usually explored in higher grades).

Line Segment: A part of a line that has two distinct endpoints. It has a definite length. A line segment between points A and B is denoted as segment AB.

Ray: A part of a line that has one endpoint and extends infinitely in one direction. A ray starting at point A and passing through point B is denoted as ray AB. The endpoint is always listed first.

Relationship: A line can be thought of as extending infinitely in both directions, a ray extends infinitely in one direction from an endpoint, and a line segment is a finite portion of a line with two endpoints.