Basic geometry: language and labels | Introduction to Euclidean geometry | Geometry | Khan Academy

Geometry originates from 'geo' (earth) and 'metry' (measurement), literally meaning earth measurement. It's the study of shapes, space, and their relationships, encompassing lines, triangles, circles, angles, patterns, and three-dimensional shapes.

A point is a basic element in geometry, representing a specific position without any dimension. Points are typically labeled with capital letters (e.g., Point A, Point B) to differentiate them. Moving from a point means no longer being on that point, thus it's considered zero-dimensional.

A line segment connects two points and includes all points in between. These connecting points are called endpoints. Line segments are one-dimensional, meaning movement is only possible along its length (back and forth). They have no width and a finite length. Line segments are denoted by their endpoints with a line drawn above them (e.g., AB). The length of a line segment AB is represented as AB without the line above.

A ray starts at a specific point (called a vertex) and extends infinitely in one direction through another point. It's a one-dimensional concept and is denoted by its starting point and another point it passes through, with an arrow over them (e.g., AD, with the arrow pointing from A to D). The order of the letters matters for rays.

A line passes through two points and extends infinitely in both directions. Unlike a line segment, a line has no endpoints. It is also a one-dimensional concept. A line is denoted by two points on it with a double-headed arrow over them (e.g., EF).

Points that lie on the same line are called colinear. A midpoint of a line segment is a point that is exactly halfway between its two endpoints, dividing the segment into two equal parts.

Two-dimensional objects, like a flat surface or a plane (an infinitely extending flat surface), allow movement in two independent directions (e.g., left/right and up/down). Three-dimensional space, which we inhabit, adds a third direction for movement (e.g., in/out of the screen). While difficult to visualize, mathematics can extend to concepts of more than three dimensions.