Geometry Definition
The word ‘geometry’ comes from two Greek words, ‘geo’ meaning earth and ‘metron’ meaning measurement. So geometry involves the measurement of all objects present on the planet Earth.
Geometry deals with the study of shapes, sizes, dimensions, angles and the position of objects around us. These shapes can be two dimensional or three dimensional. For instance, a picture or a page in a textbook is two dimensional, however, the book itself is a three dimensional object.
The most basic aspects of geometry are points, lines, angles and planes.
Types of Geometry
Depending on the type of shape, geometry can be divided into two types:
- Plane Geometry
- Solid Geometry
Plane geometry caters to the measurements and properties of two dimensional (2D) shapes such as a triangle, square, rectangle or a circle. Solid geometry on the other hand deals with three dimensional (3D) objects such as a cube, cuboid, pyramid, sphere, cylinder, cone and so on.
What is Coordinate Geometry?
Coordinate geometry deals with the study of geometric shapes by plotting them on a 2D coordinate plane. The coordinate plane is also known as the Cartesian plane. A coordinate plane is formed by the intersection of a horizontal number line called the x – axis and a vertical number line called the y – axis. When studying coordinate geometry you will study about a point, a line and a plane in greater detail.
Plotting and graphing shapes on a coordinate plane helps study their properties in a better manner and derive standard formulas.
You will learn about coordinate geometry in detail in other articles.
Geometry Formulas
As mentioned earlier, geometry helps derive standard formulas pertaining to various shapes. Here is a list of some commonly used formulas of various shapes.
Similar Objects in Geometry
Similarity is an important geometrical concept. Figures having the same shape or two shapes having the same ratio of their corresponding dimensions are called similar shapes.
The image here shows two trapezoids. So the two shapes are similar.
Congruent Shapes in Geometry
Two figures are congruent if they have the same shape and size.
You will study the congruence of triangles in detail in higher grades.
Polygons
A two dimensional shape made of straight lines is called a polygon. Figures like a triangle, quadrilateral, pentagon, hexagon and many other shapes are examples of polygons.
Here we can have a look at different types of polygons.
Polygons can be divided into two types:
- Regular polygons
- Irregular polygons
Polygons having equal or congruent sides are called regular polygons, and polygons with unequal side lengths are called irregular polygons.
Shapes that have exactly two dimensions are called two dimensional or 2D shapes. A square, circle and kite are examples of such shapes.
Shapes like a sphere, a cube or a pyramid, which have three dimensions are called 3D shapes.
A vertex is defined as a point where the edges of a solid shape intersect. The flat surfaces forming such shapes are called faces. These faces intersect each other at points called edges.
Angles are classified based on their measurements. Different types of angles include: acute angles, right angles, obtuse angles, straight angles and reflex angles.
Geometry covers a wide range of topics in mathematics including 2D and 3D shapes, symmetrical figures, coordinate geometry, area and volume measurements, similarity, congruence, finding unknown sides and angles, construction of geometric figures, angle measures and cross-sections of 3D shapes. All these topics are covered in detail in various articles on Byju’s math.