This chapter introduces us to the concept of Euclidean Geometry and how the Greek mathematician constructed the Euclid’s method who postulated some axioms and theorems. The axioms and parallel postulates are the major theories which were introduced by Euclid and it is widely recognized as a system of measurement and arithmetic.
Some of the major applications of Euclid’s Geometry are:
- Classical Geometrical problems
- Computer aided design
- Computer aided manufacturing
- Artistic designs
Download PDF of RS Aggarwal Class 9 Chapter 3 – Introduction To Euclids Geometry
The RS Aggarwal Class 9 Solutions provided below will not only help students to solve difficult questions with ease but also enable them to enhance their problem-solving skills. The solutions are explained in detailed, accurate and match the understanding level of the students. These solutions are prepared in sync with the recent syllabus of the CBSE which makes them all the more reliable and effective for exam preparation.
Exercise – 3A
Q1: What is the difference between a theorem and an axiom.
Sol: A theorem is a statement that requires a proof. Whereas, a basic fact which is taken for granted, without proof, is called an axiom.
Example of Theorem: Pythagoras Theorem
Example of the axiom: A unique line can be drawn through any two points.
Q2: Define the following terms
(i) Line segment
(iii) Intersecting Lines
(iv) Parallel Lines
(vi) Concurrent lines
(i) Line segment: The straight path between two points is called a line segment.
(ii) Ray: A line segment when extended indefinitely in one direction is called a ray.
(iii) Intersecting Lines: Two lines meeting at a common point are called intersecting lines, i.e., they have a common point.
(iv) Parallel Lines: Two lines in a plane are said to be parallel, if they have no common point, i.e., they do not meet at all.
(v) Half-line: A ray without its initial point is called a half-line.
(vi) Concurrent lines: Three or more lines are said to be concurrent if they intersect at the same point. (vii) Collinear points: Three or more than three points are said to be collinear if they lie on the same line.
(vii) Plane: A plane is a surface such that every point of the line joining any two points on it, lies on it.
Question 3: In the adjoining figure name
(i) Six points:
(ii) Five line segments:
(iii) Four rays:
(iv) Four lines:
(v) Four collinear points:
(i) Six points: A,B,C,D,E,F
(ii) Five line segments: EG, FH, EF, GH, MN
(iii) Four rays: EP, GR, GB, HD
(iv) Four lines: AB, CD, PQ, RS
(v) Four collinear points: M,E,G,B
Q4: In the adjoining figure name:
(i) Two pairs of intersecting lines and their corresponding points of intersection.
(ii) Three concurrent lines and their points of intersection.
(iii) Three rays.
(iv) Two line segments.
(i) (EF GH) and their corresponding point of intersection is R.
(AB CD) and their corresponding point of intersection is P.
(ii) (AB EF GH) and their point of intersection is R.
(iii) Three rays are: RB, RH, RG
(iv) Two line segments are: RQ, RP
(i) How many lines can be drawn to pass through a given point?
(ii) How many lines can be drawn to pass through two given points?
(ii) In how many points can the two lines at the most intersect?
(iv) If A,B,C are three collinear points, name all the line segments determined by them.
(i) An infinite number of lines can be drawn to pass through a given point.
(ii) One and only one line can pass through two given points.
(iii) Two given lines can at the most intersect at one and only one point.
(iv) AB, BC, AC
Q6: Which of the following statements are true
(i) A line segment has no definite length.
(ii) A Ray has no end point.
(iii) A line has a definite length.
(iv) A line AB is the same as line BA.
(v) A ray AB→ the same as ray BA→.
(vi) Two distinct points always determine a unique line.
(vii) Three lines are concurrent if they have a common point.
(viii) Two distinct lines cannot have more than one point in common.
(ix) Two intersecting lines cannot be both parallel to the same line.
(x) Two lines may intersect two points.
(xii) Two lines l and m are parallel only when they have no point in common.
RS Aggarwal Class 9 Solutions Chapter 3 – Introduction To Euclids Geometry
The RS Aggarwal Maths Solutions is extremely helpful in enabling students to prepare effectively for the exam. Refer to these solutions to improve your concepts and solve difficult questions with ease. The solutions are pretty detailed and given in an easy language which promotes easy learning and understanding of the concepts, enabling students to perform well in the exam. By practicing these solutions you can boost up your exam preparation.