Please refer to Introduction to Euclid’s Geometry Class 9 Mathematics Notes and important questions below. The Class 9 Mathematics Chapter wise notes have been prepared based on the latest syllabus issued for the current academic year by CBSE. Students should revise these notes and go through important Class 9 Mathematics examination questions given below to obtain better marks in exams
Introduction to Euclid’s Geometry Class 9 Mathematics Notes and Questions
The below Class 9 Introduction to Euclid’s Geometry notes have been designed by expert Mathematics teachers. These will help you a lot to understand all the important topics given in your NCERT Class 9 Mathematics textbook.
Refer to Chapter 5 Introduction to Euclid’s Geometry Notes below which have been designed as per the latest syllabus issued by CBSE and will be very useful for upcoming examinations to help clear your concepts and get better marks in examinations.
1. Euclid’s Definitions, Axioms and Postulates
2. Equivalent Versions of Euclid’s Fifth Postulate
The Greeks developed geometry is a systematic manner Euclid (300 B.C.) a greek mathematician, father of geometry introduced the method of proving mathematical results by using deductive logical reasoning and the previously proved result. The Geometry of plane figure is known as “Euclidean Geometry”.
Axioms: The basic facts which are taken for granted without proof are called axioms some Euclid’s axioms are:
(i) Things which are equal to the same thing are equal to one another. i.e. a = b, b = c⇒a = c
(ii) If equals are added to equals, the wholes are equal i.e. a = b⇒a + c = b + c
(iii) If equals are subtracted from equals, the remainders are equal i.e. a = b⇒a – c = b – c
(iv) Things which coincide with one another are equal to one another.
(v) The whole is greater than the part.
Postulates: Axioms are the general statements, postulates are the axioms relating to a particular field.
Educlid’s five postulates are.
(i) A straight line may be drawn from any one point to any other point.
(ii) A terminated line can be produced indefinitely.
(iii) A circle can be drawn with any centre and any radius.
(iv) All right angles are equal to one another.
(v) If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely meet on that side on which the angles are less than two right angles.
Statements: A sentence which is either true or false but not both, is called a statement.
eg. (i) 4+9=6 If is a false sentence, so it is a statement.
(ii) Sajnay is tall. This is not a statement because he may be tall for certain persons and may not be taller for others.
Theorems: A statement that requires a proof is called a theorem.
eg. (i) The sum of the angles of triangle is 180o .
(ii) The angles opposite to equal sides of a triangles are equal.
Corollary – Result deduced from a theorem is called its corollary.