##### Chapter 4

## Geometry

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

#### Introduction

**Algebraic Geometry:**is a geometry branch exploring multivariate polynomial zeros. This involves algebraic linear and polynomial equations that are used to solve the sets of zeros. This type of application consists of cryptography, string theory, etc.**Discrete Geometry:**The relative location of a simple geometric object, such as points, arcs, triangles, circles, etc., is concerned with it.**Differential Geometry:**using algebra and calculus methods for problem-solving. The different topics include general relativity in physics, etc.**Euclidean Geometry:**The analysis of plane and solid figures, including points, lines, planes, angles, congruence, resemblance, solid figures, focused on axioms and theorems. It has a wide variety of applications in computer science, problem-solving in modern mathematics, crystallography, etc. Also known as**Euclid’s Geometry**.**Convex Geometry**: includes Euclidean space convex forms using actual analysis techniques. It has an application in number theory for optimization and functional analysis.**Topology**: is concerned with the continuous mapping of space objects. Compactness, completeness, consistency, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, nets, proximal continuity, proximity spaces, axioms of separation, and uniform spaces are considered in its implementation.

Flat forms that can be drawn on a sheet of paper are dealt with by Plane Geometry. This involves two-dimension arcs, circles & triangles. Plane geometry is also known as the geometry of two dimensions. There are only two tests for all two-dimensional statistics, such as length and width. The width of the shapes does not interact with it. A cube, triangle, rectangle, circle, and so on are some examples of plane figures. Here, in plane geometry, some of the essential terminologies are clarified.

**Point:**A point on a plane is a particular position or spot. Normally, a dot represents them. It is necessary to consider that a point is not an item, but a location. Also, note that there is no dimension to a point; it is ideally the only place.**Line:**The line is linear (no curves), has no thickness, and continues without ending in both directions (infinitely). It is necessary to remember that to form a line, it is the convergence of infinite points together. We have a horizontal line and vertical line in geometry, which respectively are x-axis and y-axis.

A plane figure that is connected to form a closed polygonal chain or circuit by a finite chain of straight line segments closing in a circle.

The term ‘poly’ extends to multiples. An n-gon is a polygon with n sides; a 3-gon polygon is, for instance, a triangle.

General Formula for Sum of a polygon’s interior angles

Sum of a polygon’s interior angles = (n-2) x 180

**Polygon Types **

The polygon types are:

- Triangles
**Quadrilaterals**- Pentagon
- Hexagon
- Heptagon
- Octagon
- Nonagon
- Decagon

Polygon Type | Definition and Property |

Triangles | A 3-sided polygon that often adds up to 180 degrees to the number of internal angles. The area of a triangle can be found out using |

Quadrilaterals | A polygon of 4 sides with four corners and four vertices. 360 degrees sum of the number of internal angles |

Pentagon | Having five straight sides and five angles, a plane figure |

Hexagon | Having six straight sides and six angles, a plane figure |

Heptagon | Having seven sides and seven angles, a plane figure |

Octagon | Having eight straight sides and eight angles, a plane figure |

Nonagon | Nine straight sides and nine angles for a plane figure. |

Decagon | A figure of a plane of ten straight sides and ten angles. |

A Circle is a closed, simple structure. Both points in a circle are the same consistent distance from a certain point called the center, i.e. the curve drawn out by a point that travels such that the distance from the center is fixed.

**Congruence and Similarity **

**Similarity:**Whether they have the same outline or have an identical angle but do not have the same height, two figures are considered to be similar.**Congruence:**Since they have the same form and scale, two numbers are said to be congruent. They are therefore completely equivalent.

In this chapter, we learned about **lines & angles**, different shapes, and their **geometry**. We will apply this knowledge to solve questions based on **surface areas & volumes** and improvise our **constructions** of figures.

**1. What are the basics of geometry? **

Three basic concepts depend on the fundamental geometrical concepts. The point, line, and plane are them. We can’t describe the terms specifically. But, it applies to the placemark and has a definite spot.

**2. What are the 3 types of geometry? **

There are 3 geometries in two dimensions: Euclidean, spherical, and hyperbolic. For 2-dimensional objects, these are the only geometries possible.

**3. What are 10 geometric terms? **

- Perpendicular Line Segments
- Right Angle
- Equilateral Triangle
- Scalene Triangle
- Vertex
- Right Triangle
- Pentagon
- Square
- Intersecting Line Segments
- Acute Angle

**4. What are 10 geometric concepts? **

The principles in geometry are points, lines, planes, angles, parallel lines, triangles, similarity, trigonometry, quadrilaterals, transformations, circles, and area.

**5. How do we use geometry in real life?**

In the real world, geometry uses include computer-aided design for building plans, assembly systems design in engineering, nanotechnology, computer graphics, visual graphs, programming for video games, and the development of virtual reality.

We understand that learning **geometry** can be tough. At MSVgo, we provide you with easy video lessons with real-life examples to understand it easily. Go ahead and try it out now! It’s entirely free to download on the Google Play Store as well as Apple iOS App Store.