RS Aggarwal Class 9 Chapter 6 Solutions (Introduction to Euclid’s Geometry)
RS Aggarwal Solutions for Class 9 Maths Chapter 6 builds the foundation for many important geometrical terms and theorems. This chapter of RS Aggarwal Solutions for Class 9 Maths teaches you the theorems that Euclid, an Egyptian mathematician, had given on the basic concepts of geometry which is primarily used in measurements. It has 35 questions divided into 2 sets of exercises. The questions are a mix of short answer types, true and false types, and objective types which involve explanations of theorems and definitions related to geometry. Students get to know the basics of geometrical definitions like a line, concurrent and collinear points, parallel lines, incidence axioms, and opposite rays. It also acquaints you with Euclid’s work and his background and some of the important names in the field of geometry like Pythagoras and Thales.
RS Aggarwal Solutions for class 9 maths have quality questions which stimulate logical thinking in students. The solutions to these questions provided by our team would clear all your doubts on this topic as each question is explained by breaking down in simple steps for ease of understanding.
At Instasolv, our academic experts have provided the solutions in the simplest way possible. Students would learn about every topic in a way that is easy to remember and helps in better management of time.
Important Topics for RS Aggarwal Solutions for Class 9 Chapter 6: Introduction to Euclid’s Geometry
Euclid wrote a book “Elements” in which 23 definitions exist defining many kinds of lines, their intersection and angles they make. It is also composed of a number of axioms and theorems.
These lay the foundation for the concept of geometry and how they apply in daily life. Some of the important topics discussed are:
5 common notions (axioms) and 5 postulates of Euclidean geometry –
The 5 common notions are explained at the beginning of the “Elements” book, which is also called Euclid’s axioms and it states the following :
- Transitive property of Euclidean relation – If 2 things are equal to the same thing then those 2 things are also equal to one another.
- Additive property of equality – If equals are added to things which are equal then their wholes are also equals
- Subtraction property of equality – If equals are subtracted from things which are equal then their differences are also equal.
- Reflexive property – If 2 things coincide with one another then they are equals
- Whole is always greater than its parts.
The 5 postulates are like axioms i.e. they are self-evident truths which do not need proof. The creation and extension of geometric figures, using ruler and compass, comprise the 5 basic postulates of Euclidean geometry:
- Between 2 given points, a straight line segment can be drawn
- A straight line’s length can extend till infinity
- A circle can be drawn with any given point as its centre and any distance as its radius.
- Right angles are always congruent
- If a straight line falls on 2 other straight lines, so as to intersect them and if we take the angles it makes on the same side and they are less than 2 right angles then those 2 straight lines will meet if produced indefinitely towards that side on which the other straight-line makes angles which are less than 2 right angles.
Incidence axioms – Incidence geometry in its most basic form is about relations between points and lines and is expressed by phrases like “a point lies on a line”. There are 3 incidence axioms:
- Axiom 1 – Between 2 distinct points P1 and P2, only one line can be drawn
- Axiom 2 – For every line L, there are at least 2 distinct points P1 and P2 that lie on the line L.
- Axiom 3 – There exist 3 distinct points that do not all lie on the line L.
Some common geometrical terms and definitions
- Point – The most common concept of geometry, a point is defined as “that which has no part” and represented by an ordered pair (x,y) in space, here x – horizontal coordinate and y- vertical coordinate.
- Line – A breadthless length is a line
- Line segment – The shortest distance between 2 points is given by a straight path between them and that is called a line segment.
- Parallel lines – If 2 lines in a plane never meet i.e. they do not have any common points are parallel lines.
- Intersecting lines – If 2 lines have a common point then they are said to be intersecting lines.
- Concurrent lines – If 3 or more lines intersect at a common point then they are said to be concurrent lines
- Collinear points – If 3 points lie on the same line then they are called collinear points.
Exercise Discussions of RS Aggarwal Solutions for Class 9 Chapter 6: Introduction to Euclid’s Geometry
- The first set of exercises has 8 questions which are a combination of short answers and true/false type questions. You are supposed to write some of the definitions given by Euclid on common geometrical lines and points, analyze diagrams to figure out what kind of lines and rays are there.
- The 2nd set of exercises has 27 questions that test you on your knowledge on different kinds of shapes found in daily life; there are questions on Euclid’s book “Elements” and also about other famous mathematicians.
Benefits of RS Aggarwal Solutions for Class 9, Chapter 6: Introduction to Euclid’s Geometry
RS Aggarwal Solutions is very beneficial for students of class 9 to clear their concepts of Maths and revise each chapter by solving different types of questions. The Solution to these questions boost up problem-solving acumen in students by providing a clear and concise way of answering them.
Students can learn how to grasp the various theorems and formulae efficiently and also manage their time effectively by taking the help of these free online solutions from us.