Geometry begins with a handful of fundamental ideas that describe the space around us. A point is the simplest of these: it represents a single location in space but has no size, no width, no length, and no depth. Because points have no dimensions, we represent them visually with dots and label them with capital letters such as A or B. A line is the next step up; it is a straight, one-dimensional figure that extends infinitely in both directions with no thickness. Any two distinct points define a unique line, which is why two points are always collinear, meaning they lie on the same straight path.
From the idea of a line we get two related figures. A ray is a part of a line that has one fixed endpoint and extends infinitely in just one direction, like a beam of light starting at a flashlight. A line segment, by contrast, is bounded by two distinct endpoints and has a definite length that can be measured. While lines and rays go on forever, segments are finite pieces. A plane, the two-dimensional counterpart of a line, is a flat surface that extends infinitely in every direction. Three non-collinear points are always enough to define a unique plane, and any three points are automatically coplanar.
These objects also help us describe collections of points and shapes. Points are collinear if they all lie on the same straight line, and points are coplanar if they all lie on the same plane. Four or more points may or may not be coplanar, depending on whether they share a flat surface. Finally, shapes themselves can be classified by how they bend inward. A convex shape has all interior angles less than 180°, and any line segment drawn between two interior points stays entirely inside the shape. A concave shape has at least one interior angle greater than 180°, creating an indentation where a connecting segment would pass outside the boundary.