Table of contents  
Branches of Geometry  
Dimensions of Geometry  
TwoDimensional Geometry  
Measurement in Geometry 
Let us start the discussion with the different branches of geometry and learn about each of them.
In the previous header we saw the geometry basics branches, let us now understand the different dimensions of geometry in mathematics. In mathematics, objects can be categorised into no dimension objects, onedimensional, twodimensional and threedimensional objects.
A point can be visualised as a single spot or a place on a plane. It is usually specified by a dot that has no real size or shape. Hence point geometry has no dimension or we can say that it has the only position.
The line is straight and the briefest distance between two points. That is we can say that the number of points when connected makes a line geometry. As lines only possess length and no width, therefore it is counted in onedimensional shapes/objects. The different types and terms related to lines are as follows:
When two rays originate from a fixed point, then the amount of rotation from one ray to another ray is called the angle between the rays or the angle between lines. The rays are called arms of the angle. Angles are generally measured in degrees or radians. The different types of geometry angles with their definition and representation are as follows:
Plane geometry or twodimensional geometry includes flat figures like circles, rectangles, triangles and other polygons. The twodimensional objects can be drawn on paper and they hold both length and width. The different twodimensional objects with definitions and images are as follows:
Polygons
A polygon in maths is said to be a twodimensional shape. There are different names as per the sides:
Similarly, there are different other types of polygons. Refer to the below image for the same.
Triangle
A triangle is a polygon with 3 vertices say P, Q, and R which is represented as △PQR. The different types of triangles are listed in the below table.
Types of Triangles based on the Sides
Triangle can be classified into the following groups on the basis of the side of the triangle.
Types of Triangles based on the Angles
Triangles in geometry can also be classified into the following groups on the basis of the measurement of the angle of a triangle.
Quadrilaterals
A figure formed by a fourline segment is called a quadrilateral. The sum of angles of any quadrilateral is 360°. That is if the four angles of a quadrilateral are ∠A, ∠B, ∠C, ∠D. Then ∠A + ∠B + ∠C + ∠D = 360°.
The different types of quadrilaterals are listed in the below table.
The other types of polygons are:
Circles
It is the locus of all the points which lie in a plane such that their distances from a fixed point are always constant. The fixed point is called the center of the circle. A circle of center O and radius r is shown below.
The different parts of a circle are listed below:
ThreeDimensional Geometry
Solid geometry or threedimensional geometry includes objects like cubes, cuboids, prisms, cylinders, cones and spheres. All these objects hold a length, width, and height. The important characteristics of solid geometry are edges, faces and vertices. Let us understand each of them in detail.
Edges
Edges in a 3D shape join one corner point to another corner point. That is it is the line segment on the boundary that connects one vertex to the other one. They serve as the junction of two faces.
Faces
A face for 3D objects refers to the flat or curved surface of an object. For a 3D object, the face is in 2D format. A particular shape can have multiple faces.
Vertices
A point in 3D objects where two or more lines meet is said to be the vertex. Or one can understand vertices as the point of intersection of edges.
So far we read about the geometry definition, different branches, dimensions and related shapes with their images. Let us now understand the geometry formulas under the header measurement in geometry. This involved formula for the length, area, perimeter and volume calculation of different objects.
Measurement in TwoDimensional Geometry
The area and perimeter are determined using the length and bread of different geometrical objects. Some of the important geometry symbols formulas related to 2D are listed below.
Analytic geometry in twodimensional deals with the section formula, distance formula, the centroid of a triangle, the midpoint formula and so on. All these are determined using knowledge of coordinate geometry concepts.
Similarity and Congruency in Geometry
When two figures hold an identical shape or an equal angle but do not have the same size are said to be similar. If two figures have the same shape and size, then they are said to be congruent.
Measurement in ThreeDimensional Geometry
The threedimensional geometry objects or shapes as per the name are represented using 3 coordinates namely x, y and z. The formula of some important and relevant solid geometry are listed below.
Some other related concepts of solid geometry are listed below.
Direction Cosines of a Line
If a directed line say ‘R’ departing through the origin creates angles α, β and γ with x, y and zaxes, respectively, then the cosine of these angles, i.e., cos α, cos β and cos γ is termed as direction cosines of the given directed line ’R’. Direction cosines of the line joining two points: P(x_{1},y_{1},z_{1}) and Q(x_{2},y_{2},z_{2}) is given by the formula:
Direction Ratios of a Line
The directional ratios of a given line are the digits or numbers that are proportional to the direct cosines of that line. If a, b, c as the direction ratios of a line and l, m and n be the direction cosines then:
Equation of Line in 3D Geometry
If l, m, n are the direction cosines of a line passing through the point (x_{1},y_{1},z_{1}), then the equation of the line is as follows:
The equation of a line passing through the two points say; (x_{1},y_{1},z_{1}) and (x_{2},y_{2},z_{2}). Then the equation of the line is given by the formula:
Angle Between Two Lines
The angle θ between two lines whose direction ratios are proportional to a_{1},b_{1},c_{1} and a_{2},b_{2},c_{2} respectively is given the formula:
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1. What is twodimensional geometry? 
2. What are the main branches of geometry? 
3. What are some examples of twodimensional shapes? 
4. What are the properties of twodimensional shapes? 
5. How is twodimensional geometry used in real life? 

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