Geometry Key Concepts

Geometry Introduction

Etymology

• Geo: Earth (geography, geology)
• Metry: Measurement (trigonometry, metric system)
• Geometry: Earth measurement; study of shapes and space.

Basic Definitions

• Point: A position. It has zero dimensions.
• Represented by a dot.
• Labeled with letters (e.g., A, B, C).

Line Segment

• All points connecting two points (endpoints) along a straight line.
• Has a finite length (one-dimensional).
• Labeled by its endpoints with a line over them (e.g., \overline{AB}).
• AB refers to the length of the line segment.
• Endpoints: The points at the start and end of the line segment.

Ray

• Starts at a point (vertex) and extends infinitely in one direction (one-dimensional).
• Denoted with an arrow over the letters (e.g., \overrightarrow{AD}).
• The order of letters matters.

Line

• Extends infinitely in both directions (one-dimensional).
• Denoted with arrows on both ends (e.g., \overleftarrow{EF}\overrightarrow{EF}).

Collinear Points

• Points that lie on the same line.
• Example: If X, Y, and Z are on the same line, they are collinear.

Midpoint

• The point exactly halfway between two points on a line segment.
• If XZ = ZY and X, Y, and Z are collinear, then Z is the midpoint of \overline{XY}.

Dimensions

• Zero Dimensions: Point (no movement possible).
• One Dimension: Line, Line Segment, Ray (movement in one direction).
• Two Dimensions: Plane (back/forward and left/right movement).
• Three Dimensions: Space (allows movement in/out of the screen in addition to the other 2 dimensions).