Geometry Basics: Points, Lines, and Angles

Study Notes

Geometry is a branch of mathematics that deals with shapes, measurements, and relationships of points, lines, and angles.

A point is an exact location in space with no length or width.
A point has zero dimensions.
Points are labeled with a single capital letter.
In coordinate geometry, points can be plotted on a coordinate plane and located by coordinates.
The coordinate of a point is written as a point (e.g., (3, 2)).

A line is a straight set of points that continue in opposite directions forever.
A line has length, but no width, making it one-dimensional.
There are different kinds of lines in geometry, including:
- Horizontal lines: move from left to right.
- Vertical lines: move up and down.
- Perpendicular lines: intersect at a right angle.
- Parallel lines: never get closer or farther away from each other.

A line segment is part of a line with two endpoints.
A line segment does not go on forever, but has a specific beginning and ending point.
Line segments are usually labeled with two points at the endpoints.

A ray is part of a line, but it differs from a line segment.
A ray has a starting point, but it extends from that starting point in one direction forever.
A ray is identified by its starting point and another point it passes through.

An angle is created by two rays that share the same starting point (vertex).
An angle is measured by the distance between its rays in degrees.
Angles can be identified or named by their vertex or by three points on the angle.
There are different types of angles, including:
- Right angle: exactly 90 degrees.
- Acute angle: less than 90 degrees.
- Straight angle: exactly 180 degrees.
- Obtuse angle: greater than 90 degrees, but less than 180 degrees.
- Reflex angle: between 180 degrees and 360 degrees.