Introduction Basic proportionality theorem was proposed by a famous Greek mathematician, Thales, hence, it is also referred to as the Thales theorem. Triangle is one of the basic geometrical shapes with three sides & three angles. In geometry you have studied different properties & theorems of the triangle. In this tutorial, we will study one of the most important properties i.e., similarity & basic proportionality theorem. Two triangles are said to be similar if their angles are congruent & corresponding sides are in proportion. '$\mathrm{\sim}$' symbol is used to represent similar triangles. There are several methods for finding whether triangles ... Read More

Introduction Average is a single value that represents the complete group of values. Example: Average mark scored in a class is 80 %, average height in a country, average life span, average temperature in a particular area, etc. Average is classified into two groups majorly: They are mathematical average or mean and positional average. To find the positional average we can use median and mode. Average An average is the central value of the given set of values. Also, on average, the numerator is the sum of all given values, and the denominator is the total number of ... Read More

Introduction Average cost is the cost per unit manufactured in a production run. Economics is a branch of social science which studies the production, distribution & consumption of goods & services. It focuses on the behaviour & interacting economic agents & how the economy works. Cost is one of the important concepts in economics. Cost is an amount incurred for buying goods & services. The concept of cost is useful for calculating the profitable rate of operation of the firm. Also, it is useful for deciding the price of the product & sale channel. Also, it gives clarity to various ... Read More

Introduction Argument of complex number can be described as the angle made by the line formed by the complex number, with the positive x-axis of the argand plane. Argument of complex numbers describes the relationship between the imaginary and real part of the complex number. In this tutorial, we will understand complex numbers, polar form of complex numbers, argument of complex numbers, and some examples based on complex numbers. Complex Numbers Complex numbers are elements of the number system that consist of real numbers along with imaginary unit, i.e. i. which satisfies the argument; i2=-1. When a complex ... Read More

Introduction The area under a curve between two points is found out by doing a definite integral between the two points. Among the various ways to calculate the area under the curve, the most popular method is the antiderivative method. By determining the equation for the curve, the boundaries of the curve, and the axis enclosing the curve the area under the curve can be calculated. There are formulas to find the area enclosed by a circle, square, rectangle, and other polygons, but the area under the curve can be used to find area for the shapes that do ... Read More

Introduction Area of similar triangles theorem help in establishing the relationship between the areas of two similar triangles. Geometric figures having the same shape and size are known as congruent figures. Eg: Any two circles with the same radii are congruent. Any two rectangles with the same length and breadth are congruent. But, geometric figures having the same shape but different sizes are known as similar figures. The congruent figures are always similar, but two similar figures need not be congruent. Eg: Any two circles are similar. Any two rectangles are similar. Similarity of triangles is represented ... Read More

Introduction The realtion between mean , medina and mode is equal to the difference between 3 times the median and 2 times the mean. In statistics, data is a collection of information based on some natural or man-made mathematical phenomenon. There are various methods of studying data and interpreting some properties of the mathematical phenomenon, but the most common is the central tendencies. Central tendencies, as the name suggests, is a method to find the centre of all the observations in the given data in many different ways, the first is to add all the observations and divide that sum ... Read More

Introduction The relation between AM , GM and HM is written as $\mathrm{AM\times\:HM\:=\:GM^{2}}$ . When studying sequences in math, we also encounter the relationship between AM, GM, and HM. These three represent the mean or average of the corresponding series. The Arithmetic Mean (AM), Geometric Mean (GM), and Harmonic Mean (HM) are all abbreviations for mean. The mean of the arithmetic progression, the geometric progression, and the harmonic progression is represented by AM, GM, and HM, respectively. One should be familiar with these three meanings and their formulas before learning about how they relate to one another. What is Arithmetic ... Read More

Introduction A reflexive relation is a relationship between elements of a set where each element is related to the others in the set. As the name implies, every component of the set has a reflection image that is a reflection of itself. In set theory, the reflexive connection is a crucial idea. Since each set is a subset of itself, the relation "is a subset of" on a group of sets is an example of a reflexive relation. In discrete mathematics, we explore a variety of relations, including reflexive, transitive, symmetric, and others. In this lesson, we will comprehend the ... Read More

Introduction The properties of inverse trigonometric functions are associated with the range as well as domain of the function. Inverse trigonometric functions are identified as the inverse of some basic trigonometric functions such as sine, cosine, tangent, secant, cosecant, and cotangent functions. Inverse trigonometric functions are also known as, arc functions and cyclometric functions. These expressions of inverse trigonometric functions allow you to find any angle at any trigonometric ratio. These expressions are derived from the properties of trigonometric functions.It is expressed as − $$\mathrm{\sin^{-1}\:, \:\cos^{-1}\:, \:\sec^{-1}\:, \:cosec^{-1}\:, \:\cot^{-1}\:, \:and\:\tan^{-1}}$$ Inverse trigonometric functions also are known as, arc functions, and ... Read More