Geometry is the most practical branch of mathematics that deals with shapes and sizes of figures and their properties. You have already learned about the basic elements of geometry – lines and angles. Let us recall their definition.
In geometry, lines are figures that are made up of infinite points extending indefinitely in both directions. Lines are straight and have negligible depth or width.
An angle is a figure in which two rays emerge from a common point. In this article, we will discuss some more related terminologies and definitions related to lines and angles.
Lines: Basic Terms and Definitions
- A line segment is a part of a line with two end-points. It is the shortest distance between two points and has a fixed length.
- A ray is a part of a line, which has a starting point and extends infinitely in one direction.
- Collinear points are a set of three or more points which lie on the same line.
- The points which do not lie on the same line are called non-collinear points.
It is to be noted that, three points can be either collinear or non-collinear, but not both together at a same time.
Angles: Basic Terms and Definitions
- An angle is a figure in which two rays emerge from a common point. This point is called the vertex of the angle and the two rays forming the angle are called its arms or sides.
- If the arms form an angle of 90 degrees between them, it is called a right angle.
- If the inclination between the arms is less than a right angle, it is called an acute angle.
- If the inclination between the arms is more than a right angle, it is called an obtuse angle.
- If the arms form an angle of 180 degrees between them, it is called a straight angle.
- An angle which is greater than 180 degrees but less than 360 degrees is called a reflex angle.
- Two angles which sum up to 90 degrees are called complementary angles.
- Two angles which sum up to 180 degrees are called supplementary angles.
- Two angles which have a common side and a common vertex are called adjacent angles. In the following figure, ∠α and ∠β are adjacent angles.
- If two adjacent angles add up to 180 degrees, they form a linear pair of angles. In the following figure, ∠a and ∠b form a linear pair.
- When two lines intersect each other, the two opposite pairs of angles formed are called vertically opposite angles. In the following figure, ∠A and ∠B are vertically opposite angles. Another pair is ∠C and ∠D.
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