NCERT Solutions for Class 9 Maths Exercise 5.2 Introduction to Euclid’s Geometry in Hindi Medium as well as English Medium. Class 9 Maths Exercise 5.2 is now updated for CBSE and State Board students study in session 2022-2023. Questions are solved in simplified manner in Hindi and English.
NCERT Solutions for Class 9 Maths Exercise 5.2
Euclid’s Axioms and Postulates
Euclid’s main contribution was the introduction of five postulates. Axioms or postulates or the assumptions which are universal truths. Hence, they don’t require proofs. Euclid collected all the known works and raised it in book called elements having 13 chapters.
In class 9 Maths chapter 5 the focus will be on Euclid’s geometry consisting of axioms, and postulates. The most important among these is the last postulate. Postulate 1 to 4 are simple and obvious and as such not required to be proved. The terms axioms and postulates are used interchangeably.
Consistency of System of Axioms
A system of axioms are called consistent when it impossible to deduce from these axioms a statement that contradicts any axioms or previously proved statement. Using the results of axioms and postulates many theorems have been derived. A theorem is a statement which has to be proved by using definitions, axioms and reasoning. Altogether, there is chain of 465 propositions using these axioms. In exercise 5.2 there are only two questions.
Questions of Class 9 Maths Exercise 5.2
There are only two questions in 9th Maths exercise 5.2. So, it hardly needs to emphasized that both have to be done (both questions are based on postulate 5). Speaking of the 5th postulate, it can said that if a straight line cuts two straight lines in such a way that sum of the interior angles on the same side is less than 180o, the straight lines will meet on the side in which the sum of angles is less than 180o.
Euclid’s Definitions in Modern world
Euclid conceptualise and defined the terms a point, a line or plane etc. However, these are not accepted by modern mathematicians. Hence, they remained undefined. It does not mean that the contribution of Euclid was a waste. In fact, He bought a revolution in the thinking process and his contribution was able to provide framework to work upon.