What is Geometry? Everything about Geometry

Plane Geometry (Two-dimensional Geometry)

Plane Geometry deals with flat shapes which can be drawn on a piece of paper. These include lines, circles & triangles of two dimensions. Plane geometry is also known as two-dimensional geometry.

All the two-dimensional figures have only two measures such as length and breadth. It does not deal with the depth of the shapes. Some examples of plane figures are square, triangle, rectangle, circle, and so on.

The important terminologies in plane geometry are:

• Point
• Line
• Angles

Point

A point is a precise location or place on a plane. A dot usually represents them. It is important to understand that a point is not a thing, but a place. Also, note that a point has no dimension; preferably, it has the only position.

Line

The line is straight (no curves), having no thickness and extends in both directions without end (infinitely). It is important to note that it is the combination of infinite points together to form a line. In geometry, we have a horizontal line and vertical line which are x-axis and y-axis respectively.

• • • Line Segment – If a line has a starting and an endpoint then it is called a Line Segment.
    • Ray – If a line has a starting point and has no endpoint is called Ray.

Eg. Sun Rays

Angles in Geometry

In planar geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Types of Angle

Acute Angle – An Acute angle (or Sharp angle) is an angle smaller than a right angle ie. it can range between 0 – 90 degrees.

Obtuse Angle – An Obtuse angle is more than 90 degrees but is less than 180 degrees.

Right Angle – An angle of 90 degrees.

Straight Angle – An angle of 180 degrees is a straight angle, i.e. the angle formed by a straight line

Polygons in Geometry

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

The name ‘poly’ refers to multiple. An n-gon is a polygon with n sides; for example, a triangle is a 3-gon polygon.

General Formula for Sum of internal Angles of a polygon –

Types of Polygon

The types of polygons are: 

• Triangles
• Quadrilaterals
• Pentagon
• Hexagon
• Heptagon
• Octagon
• Nonagon
• Decagon

In the below figure, we can see the different types of polygons.

Circle in Geometry

A Circle is a simple closed shape. From a certain point called the centre, all points of a circle are of same consistent distance, i.e. the curve traced out by a point that moves so that its distance from the centre is constant.

Similarity and Congruency in Geometry

Similarity – Two figures are said to be similar if they have the same shape or have an equal angle but do not have the same size.

Congruence –  Two figures are said to be Congruent if they have the same shape and size. Thus, they are totally equal.

Solid Geometry (Three-dimensional geometry)

Solid Geometry deals with 3-dimensional objects like cubes, prisms, cylinders & spheres. It deals with three dimensions of the figure such as length, breadth and height. But some solid solids do not have faces (e.g. sphere).

Solid geometry is the study of three dimensions in Euclidean space. The objects which are around us are three-dimensional. All the three-dimensional shapes are obtained from the rotation operation of 2D shapes. The important attributes of 3D shapes are:

• Faces
• Edges
• Vertices

Go through these terms in detail for different geometric shapes here.

Edges

An edge is defined as the line segment on the boundary that joins one vertex to the other vertex. It means that it joins one corner point to the other. It forms the skeleton of 3D shapes.  In other words, it can be defined as the faces, that meet in the straight line is called edge. Following are the list of edges for the different solid shapes:

Faces

We know that all the geometric shapes are made up of flat surface called faces. It is a flat surface enclosed by the edges. For any three-dimensional shapes, the face should be a two-dimensional figure. The list of the number of faces for different solid shapes are given below:

Vertices

A vertex is defined as the point where the edges of the solid figure meet at each other. In other words, it can be said that, the point where the adjacent sides of the polygon meet. The vertex is the corners where the edges meet. The number of vertices for different solid shapes in  geometry is as follows: