# Geometry

Geometry (from the Ancient Greek: geo- “earth” and -metron “measurement”) is the study of properties and relations of points, lines, surfaces, and solids.

Geometric Terms:

Points are places in the space (points do not have any length, area or volume). There is a point where two lines intersect. A point is represented by a dot and named by a capital letter, eg. “point A”    •

A line is a straight path of points (extends in two opposite directions without end). A line contains infinite points.  A line is usually represented by a straight line with two arrowheads to indicate that the line goes on in both directions without stopping.   Lines can be named by two points on the line, example: Say: line  AB or  line BA

Also, lines can be named with a lowercase script letter.

Lines can intersect each other, and where they do, there is a point (point of intersection).

A Plane is a flat surface that extends forever in two dimensions (infinitely wide and infinitely long, with no thickness). A plane contains infinite points. Planes can be named by 3 points on plane, example “plane ABC”, or a capital letter  “plane G” Planes can intersect each other, and there is a line in the intersection. A line segment is a part of a line with two endpoints. A line segment has length and includes all the points between those endpoints. To name a line segment we write the endpoints in capital letters, drawing a straight line over the capital letters. Example: Say:  line segment AB  or line segment BA

The sides of a triangle are line segments. A ray starts out at a point and goes on in one direction to infinity. A ray starts at one point, called the endpoint.

We draw a small circle at the endpoint of the ray and draw an arrow at another end (1-headed arrow). An angle is made up of two rays that have the same endpoint. This endpoint is called the vertex.

## We use the symbol ∠ for angle and the letter of the vertex.  In this example ∠A (say angle A).

Also, we can name angles by using three capital letters like ∠BAC (the middle letter is the vertex of the angle)