# RS Aggarwal Solutions Class 9 Chapter 3 Introduction to Euclid’s Geometry

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## RS Aggarwal Solutions Class 9 Chapter 3 Introduction to Euclid’s Geometry

### Exercise 3A

Question 1:
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.

Question 2:
(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.

Question 3:
(i) Six points: A,B,C,D,E,F
(ii) Five line segments:  [latex]overline { EG }   [/latex], [latex]overline { FH }   [/latex], [latex]overline { EF }   [/latex], [latex]overline { GH }   [/latex], [latex]overline { MN }   [/latex]
(iii) Four rays:  [latex]overrightarrow { EP }    [/latex], [latex]overrightarrow { GR }    [/latex], [latex]overrightarrow { GB }    [/latex], [latex]overrightarrow { HD }    [/latex]
(iv) Four lines:  [latex]overleftrightarrow { AB }     [/latex], [latex]overleftrightarrow { CD }     [/latex], [latex]overleftrightarrow { PQ }     [/latex], [latex]overleftrightarrow { RS }     [/latex]
(vi) Four collinear points: M,E,G,B

Question 4:
(i) [latex](overleftrightarrow { EF } quad overleftrightarrow { GH } )  [/latex] and their corresponding point of intersection is R.
[latex](overleftrightarrow { AB } quad overleftrightarrow { CD } )  [/latex] and their corresponding point of intersection is P.
(ii) [latex]overleftrightarrow { AB }     [/latex], [latex]overleftrightarrow { EF }     [/latex], [latex]overleftrightarrow { GH }     [/latex] and their point of intersection is R.
(iii) Three rays are: [latex]overrightarrow { RB }    [/latex], [latex]overrightarrow { RH }    [/latex], [latex]overrightarrow { RG }    [/latex]
(iv) Two line segments are: [latex]overline { RQ }   [/latex], [latex]overline { RP }   [/latex]

Question 5:
(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)  [latex]overline { AB }   [/latex], [latex]overline { BC }   [/latex], [latex]overline { AC }   [/latex]

Question 6:
(i) False
(ii) False
(iii) False
(iv) True
(v) False
(vi) True
(vii) True
(viii) True
(ix) True
(x) False
(xi) False
(xii) True

Complete RS Aggarwal Solutions Class 9

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