RS Aggarwal Solutions Class 9 Chapter 3 Introduction to Euclid’s Geometry
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 axiom: A unique line can be drawn through any two points.
(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.
(viii) Plane: A plane is a surface such that every point of the line joining any two points on it, lies on it.
(i) Six points: A,B,C,D,E,F
(ii) Five line segments: , , , ,
(iii) Four rays: , , ,
(iv) Four lines: , , ,
(vi) Four collinear points: M,E,G,B
(i) and their corresponding point of intersection is R.
and their corresponding point of intersection is P.
(ii) , , and their point of intersection is R.
(iii) Three rays are: , ,
(iv) Two line segments are: ,
(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) , ,