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May 15, 2024**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.

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:

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 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

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

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).

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 |

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 |

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 × hl = length, b = breadth, h = height |

Cube | LSA: 4a^{2}TSA: 6a^{2}Volume: a^{3}a = sides of a cube |

Right Pyramid | LSA: ½ × p × lTSA: LSA + Area of the baseVolume: ⅓ × Area of the base × hp = perimeter of the base, l = slant height, h = height |

Right Circular Cylinder | LSA: 2(π × r × h)TSA: 2πr (r + h)Volume: π × r^{2} × hr = radius, h = height |

Right Circular Cone | LSA: πrlTSA: π × r × (r + l)Volume: ⅓ × (πr^{2}h)r = radius, l = slant height, h = height |

Right Prism | LSA: p × hTSA: LSA × 2BVolume: B × hp = perimeter of the base, B = area of base, h = height |

Sphere | LSA: 4 × π × r^{2}TSA: 4 × π × r^{2}Volume: 4/3 × (πr^{3})r = radius |

Hemisphere | LSA: 2 × π × r^{2}TSA: 3 × π × r^{2}Volume: ⅔ × (πr^{3})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 |

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.

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

Q. What are the basics of geometry? 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. Ans. |

Q. Is high school geometry hard? 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. Ans. |

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

Q. What are all the Geometry applications? 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.Ans. |