Pre-Calculus
- Fundamentals of Geometry
- Practical Aspects of Geometry
- Fundamentals of Trigonometry
- Practical Aspects of Trigonometry
Fundamentals of Geometry
Geometric Concepts and Terminology: Distance and Angles, Coordinates and Area
Branch of mathematics regarding geometric figures and properties of space.
Geometry is a branch of mathematics that deals with the properties, measurement, and relationships of points, lines, angles, surfaces, and solids. In this unit, we will explore the fundamental concepts and terminology of geometry, focusing on distance and angles, as well as coordinates and area.
Distance and Angles
Distance
In geometry, distance refers to the length between two points. It is always positive and is measured along the shortest path connecting the points. In a two-dimensional plane, the distance between two points (x1, y1) and (x2, y2) is given by the formula:
Distance = sqrt[(x2-x1)² + (y2-y1)²]
Angles
An angle is formed by two rays with the same endpoint. The two rays are the sides of the angle, and the common endpoint is the vertex of the angle. Angles are measured in degrees. There are several types of angles:
- Acute angle: An angle less than 90 degrees.
- Right angle: An angle that is exactly 90 degrees.
- Obtuse angle: An angle greater than 90 degrees but less than 180 degrees.
- Straight angle: An angle of 180 degrees.
- Reflex angle: An angle greater than 180 degrees.
Coordinates and Area
Coordinates
In a two-dimensional plane, each point can be identified by a pair of numbers known as coordinates. The first number (x-coordinate) represents the horizontal position of the point, and the second number (y-coordinate) represents the vertical position. The pair of numbers is often written in parentheses, like this: (x, y).
Area
The area of a shape is the amount of space it covers. It is measured in square units. Here are the formulas for the area of some common shapes:
- Rectangle: Area = length × width
- Triangle: Area = 1/2 × base × height
- Circle: Area = π × (radius)²
In conclusion, understanding these fundamental geometric concepts and terminology is crucial for further studies in geometry and other branches of mathematics. They form the basis for more complex concepts and applications, including those in calculus.