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Basic Concepts in Geometry

In this article, we will explore some basic concepts of geometry. In order to study geometry, we should know what geometry actually means. Geometry is derived from the Greek word Geometron, where ‘Geo’ means earth and ‘Metron’ means measurement; hence geometry means the measurement of earth.

The existence of geometry can be traced back to ancient times when geometry was used for various purposes such as:

  • To accurately mark the boundaries of a country or region and avoid disputes among the people.
  • Construction of magnificent temples, architecture, lakes, dams, and cities.

Further on in this article, we will study the basic terms of geometry such as points, lines, line segments, midpoints, rays, planes, and space.

Points

A point is a single dot on a piece of paper or somewhere else. A point in geometry is a location, and each location requires a name. So we name a point with a single letter or a number. A point does not have any length, width, or height. It is a zero-dimensional object.

As the article moves forward, we will see how we can derive several geometrical forms or figures with the help of Points. Refer to the below image to know how a point is named and deployed in a plane.

Lines

After points, the line is the next most basic element of geometry. Lines are basically a straight line that connects two endpoints. So, practically lines are infinite in length, but they do not have width or height. In geometry, a line is entirely straight and extends in both directions indefinitely.

Lines, just like points, are also named so that we can refer to them accordingly. Please see the graphic below to determine the figure of a line.

Types of Lines
1. Intersecting lines

If two or more lines on a plane meet at a certain point where they cut each other, they are called intersecting lines.

2. Parallel lines

If two or more lines lie on the same plane and never intersect or meet each other are known to be parallel lines.

3. Perpendicular lines

If two or more lines that lie on the same plane intersect with each other and form a 90-degree angle, they are known as perpendicular lines.

4. Skew lines
 

If two or more lines are not parallel, not intersecting, and not coplanar (i.e. they do not lie in the same plane) with each other such lines are called skew lines. This makes skew lines the most unique lines of all, and hence they can be only found in figures with three or more dimensions.

Line segment

A line segment has a beginning and an end, its starts at one point in space and ends at another. On the other hand, as we discussed previously that a line is infinite and never ends. Just like the line, the line segment also connects two endpoints, but the line segment has a finite length. Refer to the below image to know the difference between a line and a line segment.

Rays

Ray is a special type of line. A ray is a combination of a line and a line segment. Rays have beginning points but no endpoints. A ray starts at one point and goes on indefinitely in one direction. To clear any confusion, refer to the above image.

Midpoint

A midpoint is a point on a line segment that divides the line segment into two equal parts. A line segment can only have a midpoint because they have a definite length.

The figure below shows the midpoint B of the segment AC. As midpoint B divides the segment into equal parts, we can say AB=AC.

Planes

To study planes, we must know the dimensions. In our present world, there are three dimensions one dimension (1D), two-dimension (2D), three-dimension (3D).

So, as we discussed previously, a line is a one-dimensional object. That means if you practically travel on a straight line, you can only travel forward and backwards on the line. This means that you can only travel in one dimension.

On the other hand, planes are two-dimensional objects. That means you can travel forward, backward, upward, and downward. A three-dimensional object such as a cube lets you travel in all three dimensions. That means you can travel left, right, up, down, and in, out.

A plane

Planes are two-dimensional objects. A plane has length and width but no height and extends on both sides indefinitely. Planes are commonly conceived as flat surfaces, such as a tabletop. A plane is composed of an endless number of lines. 

Summary

In this article, we have covered most of the fundamental concepts in geometry, which will help you to get started with geometry as a subject. Topics that we have covered are planes, lines, line segment, rays, and midpoints. Additionally, I recommend the video below to know more about basic geometry.

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