• 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

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.