Lines and Angles - Basic Terms and Definitions

A line segment is a part of a line with two endpoints, while a ray is a part of a line with one endpoint that extends infinitely in one direction. A line extends infinitely in both directions and has no endpoints. Visually, a line segment $AB$ is a straight path connecting point $A$ to point $B$, whereas a ray $AB$ starts at $A$ and passes through $B$ with an arrow indicating it continues forever.

Collinear points are three or more points that lie on the same straight line. If they do not lie on the same line, they are called non-collinear points. Imagine three dots $A$, $B$, and $C$ placed such that a single ruler can touch all of them simultaneously.

An angle is formed when two rays originate from the same endpoint, called the vertex. The rays making the angle are called the arms. Angles are classified by their measure: Acute angle ($0^\circ < \theta < 90^\circ$), Right angle ($heta = 90^\circ$), Obtuse angle ($90^\circ < \theta < 180^\circ$), Straight angle ($heta = 180^\circ$), and Reflex angle ($180^\circ < \theta < 360^\circ$).

Complementary angles are a pair of angles whose sum is exactly $90^\circ$. Supplementary angles are a pair of angles whose sum is exactly $180^\circ$. Visually, two supplementary angles placed together side-by-side will form a straight line.

Adjacent angles have a common vertex and a common arm, but no common interior points. Their non-common arms lie on opposite sides of the common arm. Think of two rooms sharing a single wall; the wall is the common arm and the corner where they meet is the common vertex.

A Linear Pair of angles is formed when two adjacent angles have non-common arms that form a straight line. The sum of the angles in a linear pair is always $180^\circ$. This is often represented as a straight horizontal line with a single ray sticking out from a point on the line.

Vertically opposite angles are formed when two lines intersect each other at a point. These angles are always equal. Visually, this looks like an 'X' shape where the angles opposite to each other (top and bottom, or left and right) are identical in measure.