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

What is Geometry?00:00:00

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.

Points and Dimensions00:01:37

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.

Line Segments00:03:09

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.

Rays00:07:21

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.

Lines00:08:40

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).

Colinear Points and Midpoints00:10:00

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 and Three Dimensions00:11:22

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.