RD Sharma Solutions Class 9 Maths Chapter 7 Introduction to Euclid’s Geometry

RD Sharma Solutions Class 9 Maths Chapter 7: This RD Sharma Solutions for Class 9 Maths Chapter 7, you'll find everything you need to understand Euclid’s Geometry easily. This chapter introduces basic ideas like points, lines, and angles according to Euclid's rules.

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RD Sharma Solutions Class 9 Maths Chapter 7 PDF

RD Sharma Solutions Class 9 Maths Chapter 7 PDF

RD Sharma Solutions Class 9 Maths Chapter 7 Introduction to Euclid’s Geometry

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RD Sharma Solutions Class 9 Maths Chapter 7 Exercise 7.1 Page No: 7.8

Question 1: Define the following terms.

(i) Line segment

(ii) Collinear points

(iii) Parallel lines

(iv) Intersecting lines

(v) Concurrent lines

(vi) Ray

(vii) Half-line

Solution:

(i) Line segment: A line segment is a part of a line that connects two points, serving as the shortest distance between them. Essentially, it's a one-dimensional shape.

(ii) Collinear points: When two or more points lie on the same line, we say that they are collinear.

(iii) Parallel lines : Parallel lines in a plane are lines that don't intersect each other.

(iv) Intersecting lines: Two lines intersect when they meet at a common point, known as the point of intersection.

(v) Concurrent lines: Two or more lines are said to be concurrent if there is a point which lies on all of them.

(vi) Ray: A straight line extending from a point indefinitely in one direction only.

(vii) Half-line: If A, B. C be the points on a line l, such that A lies between B and C, and we delete the point A from line l, the two parts of l that remain are each called a half-line.

Question 2:

(i) How many lines can pass through a given point?

(ii) In how many points can two distinct lines at the most intersect?

Solution:

Question 3:

Solution:

Question 4: Write the truth value (T/F) of each of the following statements:

(i) Two lines intersect in a point.

(ii) Two lines may intersect in two points.

(iii) A segment has no length.

(iv) Two distinct points always determine a line.

(v) Every ray has a finite length.

(vi) A ray has one end-point only.

(vii) A segment has one end-point only.

(viii) The ray AB is same as ray BA.

(ix) Only a single line may pass through a given point.

(x) Two lines are coincident if they have only one point in common

Solution:

(i) False

(ii) False

(iii) False

(iv) True

(v) False

(vi) True

(vii) False

(viii) False

(ix) False

(x) False

Question 5: In the below figure, name the following:

(i) Five line segments

(ii) Five rays

(iii) Four collinear points

(iv) Two pairs of non–intersecting line segments

Solution:

(i) Five line segments AB, CD, AC, PQ. DS

(ii) Five rays :

(iii) Four collinear points. C, D, Q, S

(iv) Two pairs of non–intersecting line segments AB and CD, PB and LS.

Question 6: Fill in the blanks so as to make the following statements true:

(i) Two distinct points in a plane determine a _____________ line.

(ii) Two distinct ___________ in a plane cannot have more than one point in common.

(iii) Given a line and a point, not on the line, there is one and only _____________ line which passes through the given point and is _______________ to the given line.

(iv) A line separates a plane into _________ parts namely the __________ and the _____ itself.

Solution:

(i) unique

(ii) lines

(iii) perpendicular, perpendicular

(iv) three, two half planes, line.

RD Sharma Solutions Class 9 Maths Chapter 7 VSAQs Page No: 7.9

Question 1: How many least number of distinct points determine a unique line?

Solution : Two

Question 2: How many lines can be drawn through both the given points?

Solution : One

Question 3: How many lines can be drawn through a given point?

Solution : Infinite

Question 4: In how many points two distinct lines can intersect?

Solution : One

Question 5: In how many points a line, not in a plane, can intersect the plane?

Solution : One

Question 6: In how many points two distinct planes can intersect?

Solution : Infinite