Geometry - Basic Geometrical Ideas: Points, Lines, Angles, Curves, Polygons

A Point is a mark of position, represented by a tiny dot and named with a capital letter (e.g., Point $A$). A Line Segment $\overline{AB}$ is the shortest path between two points $A$ and $B$, having a fixed length. A Line $\overleftrightarrow{PQ}$ is a straight path that extends infinitely in both directions, visually represented by arrows at both ends.

A Ray $\overrightarrow{OX}$ is a part of a line that starts at a fixed point $O$ (called the starting point or origin) and extends infinitely in one direction, much like a beam of light from a torch.

Intersecting Lines are two lines that meet at a single common point, forming a cross or 'X' shape. Parallel Lines are lines in the same plane that never meet, no matter how far they are extended, like the opposite edges of a rectangular ruler or railway tracks.

Curves are shapes drawn without lifting the pencil. A Simple Curve does not cross itself. An Open Curve has different starting and ending points, whereas a Closed Curve starts and ends at the same point, enclosing an interior region.

A Polygon is a simple closed curve made up entirely of line segments. The segments are called 'sides', the points where two sides meet are 'vertices', and a line segment joining two non-adjacent vertices is called a 'diagonal'. For example, a triangle has 3 sides and 3 vertices, while a quadrilateral has 4 sides.

An Angle is formed by two rays (called arms) meeting at a common endpoint (called the vertex). It is denoted by the symbol $\angle$. In $\angle ABC$, the vertex $B$ is always written in the middle. The region between the two arms is the interior of the angle.

A Circle is a simple closed curve where every point on the boundary is at an equal distance from a fixed center point $O$. The distance from the center to any point on the boundary is the Radius ($r$). A Chord is a segment joining any two points on the circle, and the Diameter ($d$) is the longest chord that passes through the center.

A Circle is divided into parts: an Arc is a portion of the boundary; a Sector is the region enclosed by an arc and two radii; and a Segment is the region enclosed by an arc and a chord.