In geometry, everything starts somewhere. But what if the starting points themselves can't be defined? That's the case with three fundamental concepts: the point, the line, and the plane. We can't define them using other terms because there's nothing more basic. Instead, we describe them.

A point is a location. It has no size, no width, no length, no depth. It's represented by a dot and named with a capital letter, like point A.

A line is a straight path that extends infinitely in two directions. It has no thickness. A line is defined by two points, and you name it using those two points, like line AB ($\"{AB}$), or sometimes with a single lowercase letter, like line $l$.

A plane is a flat surface that extends infinitely in all directions. Think of a sheet of paper that goes on forever. It's defined by three points that are not on the same line. You name a plane by three of its points, like plane ABC, or with a single capital script letter, like plane $\\textit{P}$.

These are the building blocks. Every shape, solid, and complex figure you'll encounter in geometry is constructed from some combination of points, lines, and planes. This axiomatic approach, where we start with a few accepted, undefined truths, is a powerful idea championed by the ancient Greek mathematician Euclid over two thousand years ago.

Once we have our undefined terms, we can start defining other concepts. These are the first pieces we build from our basic set.

A line segment is a part of a line that consists of two endpoints and all the points between them. Unlike a line, a segment has a finite length. We name it by its endpoints, like segment AB ($\"{AB}$). Note the bar on top has no arrows.

A ray is a part of a line that starts at one endpoint and extends infinitely in one direction. Think of a ray of light from the sun. We name it by its endpoint first, then another point on the ray, like ray AB ($\"{AB}$). The arrow on top shows the direction of infinity.

An angle is formed by two rays that share a common endpoint, called the vertex. The rays are called the sides of the angle. You can name an angle in a few ways: by its vertex (if it's the only angle with that vertex), by a number placed inside the angle, or by three points, with the vertex always in the middle. For example, we could call an angle $\angle B$, $\angle 1$, or $\angle ABC$.

Now that we have names for these pieces, we need rules for how they interact. In geometry, these fundamental rules are called postulates or axioms. We accept them as true without proof. They are the agreed-upon starting points for logical arguments.

One of the first is the Segment Addition Postulate. It's quite intuitive. If you have three points A, B, and C that are collinear (all on the same line), and B is between A and C, then the length of segment AB plus the length of segment BC equals the length of the whole segment AC.

Let's say AB = 5 cm and BC = 8 cm. According to the postulate, the length of the entire segment AC must be 5 + 8 = 13 cm. This simple rule is powerful for solving for unknown segment lengths.

Similarly, the Angle Addition Postulate works for angles. If a point B lies in the interior of $\angle AOC$, then the measure of $\angle AOB$ plus the measure of $\angle BOC$ is equal to the measure of the whole angle, $\angle AOC$.

So, if $AB = CD$, we write $\overline{AB} \cong \overline{CD}$. If $m\angle PQR = m\angle XYZ$, we write $\angle PQR \cong \angle XYZ$. This distinction between equality (for measures, which are numbers) and congruence (for figures, which are geometric objects) is a crucial detail in formal proofs you'll encounter later.

These terms and postulates are the alphabet and grammar of geometry. Mastering them allows you to read, write, and understand the language of shapes and space.