Important Properties of Similar Triangles

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In 2022, a significant change was introduced by the Ministry of Education in the exam conducting body of India’s toughest entrance exams- JEE Main and JEE Advanced. The tests will now be administered by a new committee known as the JEE Apex Board (JAB). Students should browse the official online portal on a frequent basis to ensure that they do not miss any vital updates. As per the latest notification, the exams will be conducted in June and July. Earlier, it was scheduled for April and May. But to avoid a clash of dates of board exams of different states, the exam was postponed to June and July. This also ensures that all students get a chance to attempt the JEE after their board exams.

Students should always have a good understanding of the syllabus when studying for the JEE exam. They should be aware of what they should and should not learn. In terms of the JEE exam, properties of similar triangles are a significant subject. There are many important theorems related to similar triangles. In this article, we will discuss similar triangles, properties and derivatives.

Similar Triangles

Similar triangles are triangles that have a similar appearance but a change in size. While two objects have the same shape and differ in size, they are considered to be similar. Similar shapes overlap each other when enlarged or demagnified. Similarity describes the fact of similar shapes.

Formula for similar triangles in geometry

Let JKL and STU be two triangles. Then

∠J = ∠S ∠K = ∠T and ∠L = ∠U,

JK/ST = KL/TU = JL/SU.

If the corresponding angles of two triangles are equal and their corresponding sides are within the same ratio, they are similar. When two triangles’ corresponding angles are identical, the triangles are similar.

Theorems

The similarity theorems can be used to determine or prove whether two triangles are similar. When we don’t have the length of all the triangle’s sides or the length of all its angles, we apply these similarity conditions. These theorems help us to rapidly determine whether or not two triangles are similar. There are three major types of similarity rules. Students should not get confused with similar triangles and congruent triangles. Thorough learning of the concepts will help students to easily crack similar triangle problems.

Derivative of a function

Derivatives have great importance in Calculus. A derivative is the rate at which a function changes in relation to another quantity. In calculus, differentiation refers to the process of determining a function’s derivatives. Calculus’ main principles are finding derivatives and integration.

Sir Isaac Newton established the laws of differential calculus. Many scientific areas employ the concepts of limits and derivatives. Students can expect 2-3 questions from derivatives for the JEE Main and the JEE Advanced.

The JEE aspirants can find out previous years’ questions and solutions on derivatives online and learn them. Free PDFs are available in many web portals. Students can also make use of the videos regarding derivatives which are available online. Visit BYJU’S to learn more about similar triangles and derivatives.