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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

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