# Geometry Basics - Basic Geometry Concepts & Definitions

By the end of this lesson, you will be able to

- define geometry.
- describe basic geometry definitions.
- interpret basic geometry concepts.
- distinguish plane geometry and solid geometry.
- identify basic geometry shapes.
- build a solid shape from the origin.
- analyse geometric dimension.
- explain Euclidean definitions, axioms and postulates.

## What is Geometry

The branch of mathematics where shapes and size, relative position of figures and solids, spatial relationships and properties of space are discussed and analysed is called geometry.

A rectangle is moving around a circle.

Here space means 3-dimensional space that extends in direction length, breadth and height infinitely far. Therefore, shapes and size, finding out relative position among objects are the part of geometry.

Geometry is one of the oldest branch of mathematics. In ancient Greek, geo means earth and metron means measurement. The combination of these two words form geometry means earth measurement or land measurement. From that point of view, it is estimated that the ancient Greek people used to apply geometry to measure their land.

## Basic Geometry Concepts

Geometry is the structure of objects in terms of shape and size.

Are you interested in playing with objects in different shapes and sizes or love to drawing and sketching?

If so, introduction to geometry basics lesson is perfect for you. Let's go to learn simple geometry step by step.

Wait..! Would you mind if this elementary geometry basics lesson is explained explicitly. Well.

Basic geometry study is the part of geometry discusses root elements of geometry that forms all geometric shapes and sizes. It helps understanding geometry for beginners.

Basic geometry concepts includes the fundamental concepts of

- Point
- Line
- Intersecting lines
- Parallel lines
- Perpendicular lines
- Ray
- Line segment
- Angle
- Curve
- Perimeter
- Surface
- Plane
- Area
- Space and Solid

## Basic Geometry definitions

Basic geometry includes point, line, plane, angle, curve, surface (plane or curved surface) and solid.

### Point

In Euclidean geometry, point is the notion of a unique location. It is one of the most fundamental objects on which the geometry is built. That is why, it is impossible to define a point depending upon previously defined objects in geometry.

When two lines intersect, a point is produced. That is, the position at which two lines intersect is called a point. By meeting Two edges of a book, for example, a point is produced.

In mathematics, a point is considered as a unique position. That is a point is nothing but a position. A point does not have any length, width or height. It has no part. So, a point is has no dimension.

One and only one line can be drawn by adding two distinct points on a plane.

Point can be defined another way in terms of line. If one reduces the length of a line step by step, at last it produces a point. Space is the set of all points.

### Line

A line is the set of points that extends along a straight path infinitely on and on its opposite direction.

Another way ...

A line is a continuous extent of straight length infinitely far on and on its opposite direction without width or depth.

So a line, strictly speaking, is perfectly straight and has no ends in both directions. The path of line is straight. So, a line is well-known as straight line.

A line is shown in the figure that extends infinitely in both directions. It has no end points. It has only length. Thus, a line is of one dimension and sometimes called one d.

Suppose A and B are two distinct points on a line. It is read AB is a line is denoted by

The study of line in geometry basics includes:

- intersecting lines
- parallel lines
- perpendicular lines

### Intersecting Lines

Two or more distinct lines are called intersecting lines if they have a common point. Two intersecting lines can intersect only at a unique point. Consequently, intersecting lines cannot have more than one common point. In a nutshell, all intersecting lines share a point.

### Parallel Lines

Two or more distinct lines are called parallel if there does not exist any common point. Parallel lines never intersect to each other.

Another way, two distinct lines are called parallel lines if they always maintain equal distance between them. In plane geometry, parallel line do not meet to each other. They never share a common point.

### Perpendicular Lines

Two lines are called perpendicular if they meet at a right angle to each other. In the same way, two lines are said to be perpendicular if they form an angle equal to 90^{0} between them. Perpendicular lines obviously express the relation between them in terms of angle.

Another way, a line is called perpendicular to another line if they they form an angle of 90^{0}.

The study of line in basic geometry also includes:

- ray
- line segment

### Ray

A ray is the part of a line that starts from a fixed point and goes on infinitely far only in one direction. A ray is also sometimes called a half-line. It has an endpoint.

The point p is called the end point in both figures.

### Line Segment

A line segment is a definite part of a line having two endpoints. Line segment may contains endpoints or not. There are three types of line segments in terms of containing endpoints such as:

- closed line segment
- open line segment
- half-open line segment

### Line Segment Example

#### Closed Line Segment

A line segment is said to be closed if it contains both endpoints.

#### Open Line Segment

A line segment is said to be open if it excludes both endpoints.

#### Half-open Line Segment

A line segment is called half-open if it contains only one endpoint.

To deep dive about line segment and ray, you can have a look two seperate complete tutorials on ray and line segment.

### Angle

A figure formed by two rays, inclination to each other, sharing a common endpoint is called an angle. The rays are known as the sides of the angle and the common endpoint is called the vertex of the angle. The measurement of angle is equal to how much two rays or sides are inclined to each other.

An acute angle is shown in figure.

In figure, ray OA and ray OB is inclined to each other and meet sharing a common a point O. As a result, an angle ∠AOB is formed at the point O. This is an acute angle because it is less than a right angle or 90°.

### Curve

A curve is a smoothly-flowing path that may be straight or not. If the curve is straight, it is a line. So, a line is always a special type of curve. On the contrary, a curve is a generalization of line. Again, if the curve is not straight, it always changes its directions.

A curve is a one dimensional figure. So, a curve is included in one dimensional geometry.

### Perimeter

In plane geometry, perimeter is the length of the outline of a two dimensional shape. It is the sum of the length of all sides of a shape. In a nutshell, it is the distance around a shape. Sum of the length of three side, for example, is the perimeter of a triangle. The perimeter of a wheel or circle is called circumference. Hence, the circumference of a circle is the length of outer side of the circle.

### Surface

Surface is one of the most important and fundamental parts of basic geometry. A surface is a two-dimensional figure that may be flat or not. A circle, for instance, is a flat surface whereas outer part of a sphere is a curved surface. Thus a surface is a generalization of plane; as the plane is a flat surface. On the contrary, a plane is a special case of surface. Surface is discussed and analyzed in 2-dimensional geometry.

### Plane

If one arranges a set of lines one after another, it produces a plane.

A plane is all about two dimensional flat surface that expands infinitely. Plane is the part of two dimensional geometry.

The two dimensions are length and width.

The length and width must lie on the same plane.

Thus, a plane has two dimensions.

All 2d shapes lie on the plane.

Three parallel planes are shown in the figure.

Three parallel planes are in 3 different levels.

### Area

Basic geometry concepts includes the area of surface. Area is the definite part of a surface. A surface consists of two dimension namely length and breadth. Thus area is related to two dimensional geometry. The area of a rectangle, for instance, means how much surface the rectangle contains.

### Space and Solid

Space is the set of all 3-dimensional points. Space consists of infinite number of points as well as infinite number of planes. In a nutshell, space is the 3-dimensional boundless extent.

Therefore, all objects in space have the relative position and direction.

And any object in space is called solid. Again, several planes can make a solid. Six congruent square planes, for example, form a cube.

### Geometric Dimensions

Basic geometry concepts discusses the dimension of geometric shapes. Understanding geometric dimension, there can have a review of point, line, plane and solid.

A point is nothing but a position. It has no length or width. So, a point is of no dimension or zero dimension.

A line is the set of points that extends along a straight path infinitely on and on its opposite direction. It has only length (breadthless length). So, a line is of 1 dimension or simply one d.

A plane is the two dimensional flat surface that goes on infinitely. It has only length and width. So, a plane is of two dimension.

A solid has length, width and height or depth. So, a solid is of 3 dimensional geometric shapes.

Therefore, a clear concept of geometrical dimension is must to understand high school geometry.

Geometry discusses the relative position of figures. Basic geometry includes dimension. Zero dimensional or no dimensional geometry is concerned with point. A point is nothing but a position. It has no length, width or heigth. One dimensional geometry is relevant to distance. Because it has only length. Two dimensional geometry is invloved all about area. Because it has only length and width. And 3 dimensional geometry is invloved with volume or space. As volume or space consists of length, width and height.

### Formation of Shapes in Different Dimensions

## Euclidean Geometry

Euclid wrote a textbook namely 'Elements'. There are 13 books in Elements. Euclid defined some basic geometric elements like point, line and surface at the very beginning in his book I. Although some of his definitions in modern mathematics has a limitation, that are stiil the foundation of geometry.

### Euclidean Definitions

Euclidean definitions are given below:

- A point has no part.
- A line has no ends.
- Euclid defined general line is a "breadthless length". This line may be stright line or curved line.
- A line has only length but it has no breadth or height.
- The line on which points are on straight or same direction is straight line.
- A surface has length and height.
- The edge of surface is line.
- The surface on which the straight lines are flat is plane.

### Euclidean Axioms

In mathematical analysis, some results are considered to be true. This is well-known axioms. Euclid considered some results that are always true and these results are known as Euclidean axioms.

Some Euclidean axioms are given below:

- All things those are equal to the same thing are equal to each other.
- If same is added to equals, the sums are equals to one another.
- If same is subtracted from equals, the results are equal.
- All things coincide to each other are equal to each other.
- The whole is always larger than its part.

### Euclidean Postulates

In modern geometry point, line and surface are taken as elementary concepts in basic geometry and considered some of their properties are obviously true. And these are familiar to Euclidean postulates.

Some Euclidean postulates are given below:

- Only one line can be true from a point to another point.
- Finite straight line can be produced continuously on a line.
- Circle can be drawn with any center and any radius.
- All right angles are equal to each other.
- If a stright line intersects to other straight lines make a couple of interior angles smaller than two right angles, they must intersects on that side on which the angles are smaller than two right angles.

## Basic Geometry in terms of measurement

Geonerally, Geometry is generally divided into two parts in terms of measurement.

### Plane Geometry

Plane geometry is the two dimensional geometry. Plane geometry is, in fact, formed with two dimensional geometric shapes. It is all about the geometry of two dimensional geometric shapes. Basic geometry elements, for instance, points, lines, angles, surfaces, area are discussed in plane geometry.

In mathematics, plane geometry generally refers to Euclidean plane geometry./p>

Point, line, triangle, quadrilateral, cilcle, ellipse, parabola, hyperbola all are basic geometry shapes under plane geometry. Any plane geometric shape can be drawn on a piece of paper. The position, lenght, perimeter, area of plane geometric figures are measured here. Plane geometry is also familiar with high school geometry as it is taught in secondary schools all over the world. So, this geometry lessons are helpful for those people who are involved in teaching and learning geometry in institution.

### Solid Geometry

Solid geometry is the 3-dimensional geometry. So, solid Geometry deals with shapes and figures of 3 dimensional space. Three dimension means length, breadth and height. Different types of solid objects are discussed in solid geometry.

Thus a solid is of 3 dimensional object.

It mainly discusses the measurements, specially the volume of solid shapes.

Cuboid, cube, cone, cylinder, prism, pyramid, sphere all are solid objects and they are formed in 3-dimensional space.

A cube is showing its faces, edges and vertices.

A list of basic geometric shapes names are given below:

- plane geometry
- point
- curve
- line
- line segment
- ray
- length
- angle
- triangle
- scalene triangle
- isosceles triangle
- equilateral triangle
- acute triangle
- obtuse triangle
- right triangle
- quadrilateral
- trapezoid
- isosceles trapezoid
- parallelogram
- kite
- rhombus
- rectangle
- square
- polygon
- pentagon
- hexagon
- octagon
- circle
- ellipse
- parabola
- hyperbola

- solid geometry