Exams Academic Geometry: Definition, Shapes, Structure, Examples

Written By Vaibhav_Raj_Asthana
Last Modified 15-03-2024

Geometry: Definition, Shapes, Structure, Examples

Geometry is a branch of mathematics that is largely concerned with the forms and sizes of objects, their relative positions, and the qualities of space. The word Geometry is derived from the Ancient Greek word were geo- “earth,” -metron “measuring”. Euclid, the Greek mathematician who is known as the “Father of Geometry,” developed a number of postulates and theorems.

Geometry is a discipline of mathematics that connects distances, angles, patterns, areas, and volumes using mathematical concepts. Geometry is the general concept for all visually and spatially related topics. On this page, let’s take a look at all of the major themes in Geometry. Read further to find more.

Geometry: 2D And 3D Shapes

2d shapes are plane figures that can be drawn on a piece of paper. Some examples of 2d figures are given below:

3d shapes are those which can be represented in 3d space and can be solid as well as hollow. Some 3d figures are given below:

What Is Plane Geometry?

Plane Geometry involves those shapes and figures that can be drawn on a piece of paper just like 2d figures. It is also referred to as 2d geometry wherein calculations are based on the length and breadth of the figures. Circle, rhombus, square are examples of plane geometry.

Point

A point or a dot is a location or a place on a plane that is dimensionless, sizeless and only has a position. There can be single or multiple points in a plane.

Line

The figure below shows a line. It has no end points and extends to infinity towards both the ends.

Ray

Ray is a type of line which has one fixed point and extends to infinity towards the other. XY is the ray in the below figure.

Line Segment

A line segment is a type of line that has fixed points and is not infinite on either end.

Angles In Geometry

Angles are formed when two rays emerge from a common point. An angle can vary from 0° to 360°. Various shapes form various angles; for example, all the angles in a square and rectangle are 90°.

Angles are of 5 types:

i) Acute Angle
ii) Obtuse Angle
iii) Right Angle
iv) Straight Angle

Polygons In Geometry

Closed figures formed by line segments which are represented in a plane are called Polygons. These figures have a minimum of 3 lines (sides) and can have n number of maximum lines. The point where two lines join to form an angle is called a vertex.

Types Of Polygons

i) Triangles
ii) Quadrilaterals
iii) Pentagon
iv) Hexagon
v) Heptagon
vi) Octagon
vii) Nonagon
viii) Decagon

Geometry Polygons — Polygons with angles

Coordinate Plane: X-Axis And Y-Axis

A plane formed when two lines intersect each other at right angles (90°) is called a coordinate plane. This is usually used to draw bar graphs, charts, etc.

The point where two axis intersect is called origin (0,0). Any point on the X-axis line will have 0 value of y (a,0) and any point on Y axis will have 0 value of x (0,y).

If the point lies above X and Y axis the it will have both the values and will be represented as given in the above image A(25,25).

Edges, Faces, & Vertices In Geometry

Below we have tabulated some facts on the number of edges, the number of faces as well as the number of vertices in various geometrical figures.

Edges In Geometry

Shape	Number of Edges
Triangular Prism	9
Cube	12
Rectangular prism	12
Pentagonal Prism	15
Hexagonal Prism	18
Triangular Pyramid	6
Square Pyramid	8
Pentagonal Pyramid	10
Hexagonal Pyramid	12

Practice 12th CBSE Exam Questions

Vertices In Geometry

Shapes	Number of Vertices
Triangular Prism	6
Cube	8
Rectangular prism	8
Pentagonal Prism	10
Hexagonal Prism	12
Triangular Pyramid	4
Square Pyramid	5
Pentagonal Pyramid	6
Hexagonal Pyramid	7

Faces In Geometry

Shapes	Number of Faces
Triangular Prism	5
Cube	6
Rectangular prism	6
Pentagonal Prism	7
Hexagonal Prism	8
Triangular Pyramid	4
Square Pyramid	5
Pentagonal Pyramid	6
Hexagonal Pyramid	7

Geometry Symbols

Below we have provided some basic symbols that are used in geometry to represent objects or things.

Symbol	Symbol Name
∠	Angle
∟	Right angle
° or deg	Degree
′	Prime
″	Double prime
___	Line
AB	Line segment
—>	Ray
⊥	Perpendicular
∥	Parallel
≅	Congruent to
~	Similarity
Δ	Triangle
\|x–y\|	Distance
π	Pi
^c or rad	radians
^g or grad	gradians / gons

Geometry Formulas

In thsi section, we have provided the basic geometry formulas that will aid you in preparing for the topic. We will use the following abbreviations for convenience:

1. LSA – Lateral/Curved Surface Area
2. TSA – Total Surface Area

Name of the Solid Figure	Formulas
Cuboid	LSA: 2h(l + b) TSA: 2(lb + bh + hl) Volume: l × b × h l = length, b = breadth, h = height
Cube	LSA: 4a² TSA: 6a² Volume: a³ a = sides of a cube
Right Pyramid	LSA: ½ × p × l TSA: LSA + Area of the base Volume: ⅓ × Area of the base × h p = perimeter of the base, l = slant height, h = height
Right Circular Cylinder	LSA: 2(π × r × h) TSA: 2πr (r + h) Volume: π × r² × h r = radius, h = height
Right Circular Cone	LSA: πrl TSA: π × r × (r + l) Volume: ⅓ × (πr²h) r = radius, l = slant height, h = height
Right Prism	LSA: p × h TSA: LSA × 2B Volume: B × h p = perimeter of the base, B = area of base, h = height
Sphere	LSA: 4 × π × r² TSA: 4 × π × r² Volume: 4/3 × (πr³) r = radius
Hemisphere	LSA: 2 × π × r² TSA: 3 × π × r² Volume: ⅔ × (πr³) r = radius

Also, check other study resources from Embibe:

Maths Formulas For Class 8	Maths Formulas For Class 10
Trigonometry Table	Trigonometric Ratios
Mensuration Formulas	Algebra Formulas

Summary

Geometry is a branch of mathematics concerned with the forms, angles, dimensions, and sizes of a wide range of objects seen in daily life. Geometry is derived from two Ancient Greek words: ‘geo’ which means ‘Earth,’ and ‘metron’ which means ‘measurement.’ There are two-dimensional and three-dimensional forms in Euclidean geometry.

Flat shapes are 2d shapes such as triangles, squares, rectangles, and circles in plane geometry. Solids are 3D forms such as a cube, cuboids, cones, and others in solid geometry. Coordinate geometry explains how points, lines, and planes are used in fundamental geometry.

Geometry’s many forms of shapes help us in understanding the shapes we encounter in daily life. We can compute the area, perimeter, and volume of forms using geometric ideas.

Frequently Asked Questions: FAQs

Here are some questions that are mostly searched on the topic:

Q. What are the basics of geometry?
Ans. Basics of any topic refer to the general concepts and theories that are necessary for understanding concepts. In this case, it involves angles, vertices, plane, line, line segment, shapes, etc.

Q. Is high school geometry hard?
Ans. A topic or a subject can be hard or easy depending upon how you understand it. If you have all the resources, the formulas are at your fingertips, and your concepts are clear, things become really easy in geometry. All you need to do is clear your basic concepts.

Q. What is geometry?
Ans. The word geometry has been derived from the Greek word “Geo” and “Metry”. Geo means earth and Metry means measurement.

Q. What are all the Geometry applications?
Ans. Geometry has a wide range of applications from ancient times till now and will be valid in future as well. All constructions are done using geometrical concepts, data evaluation, projection of things, navigation, MRI, etc.