Geometry Basics: Points, Lines, Planes, Angles, and Measurement Units

Study Notes

Geometry: Points, Lines, Planes, Angles, Measurement Units

Points, Lines, Planes

In geometry, points are exact locations in space. They are represented by dots and are used to represent a particular location in diagrams and graphs. Points do not have width, length, or height and so they do not have any dimension. Points are usually labeled in capital letters.

A line is formed by infinite points that extend on both sides. Unlike points, lines have length and so they are one-dimensional objects. Lines are used to represent a straight path between two points, which extends infinitely in both directions. They are flat and have no width. Lines can be named by drawing a horizontal arrow above two points in the line. For example, a line with points C and D would be written like \overleftrightarrow{CD} or \overleftrightarrow{DC}.

A plane is a flat two-dimensional surface that extends infinitely in every direction. Planes may be named by giving them a capital letter, or by listing any three points on the plane in any order. Points that are on the same plane are called coplanar points.

Angles

An angle is formed when two rays are joined together at a common point. The common point here is called the node or vertex and the two rays are called the arms of the angle. The angle is represented by the symbol ' ∠'.

The angle is usually measured in degrees, using a protractor. Degrees 30°, 45°, 60°, 90°, 180° show different angles. The types of angles are based on the values of angles in degrees. We can also represent angles in radians, i.e., in terms of pi (π). 180 degrees is equal to π in radians.

Measurement Units

Angles are measured in degrees, which is a unit of measurement. The degree is represented by the symbol °. It is based on the Babylonian number system, which used a base 60 (Sexagesimal) system. In their calendar, there were a total of 360 days, so they adopted a full angle to be 360°. They then divided a full angle into angles using the angle of an equilateral triangle and further divided a degree into minutes and seconds.

1° = 60′ = 3600″

In addition to degrees, angles can be measured in radians, which is the SI unit of angle. Radians are mostly used in calculus. The length of the arc of a unit circle is numerically equal to the measurement in radian of the angle that it subtends. In a complete circle, there are 2π radians.

1 radian = 180°/π

Another unit of measurement for angles is the gradian or grad. An angle is equal to 1 gradian if the rotation from the initial to the terminal side is 1/400 of the full rotation. The full angle is equal to 400 gradians. The gradian is denoted by the symbol 'grad'.

1 gradian = 1/400 of a full angle

In conclusion, geometry is a branch of mathematics that deals with the properties and relationships of points, lines, angles, surfaces, and solids. It involves understanding the properties of these basic geometric shapes and how they are used to describe the world around us.

Description

Learn the fundamentals of geometry, including definitions and properties of points, lines, planes, and angles. Understand how to measure angles in degrees, radians, and gradians. A comprehensive introduction to basic geometric concepts.