Class 9 RD Sharma Solutions – Chapter 7 Introduction to Euclid’s Geometry- Exercise 7.1

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) A line segment is a one-dimensional line connecting two points. It is the shortest distance that is incident on both the points.

(ii) Two or more points incident on the same line are called collinear points. 

(iii) Parallel lines run opposite each other and do not intersect each other at any point of time. 

(iv) Intersecting line segments are a pair of lines meeting each other at a common point, which is also called a point of intersection. Both the lines are incident on this point.

(v) Two or multiple line segments that are incident on a common point, are called concurrent lines.

(vi) A ray is a line segment that is fixed on one end and indefinitely extending on the other. 

(vii) Let us assume A, B, C be the points on a line, such that A lies mid-way between B and C. If we delete the point A in between from B and C from the line, the two parts of l 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:

(i) An infinitely large number of lines can pass through a given point

(ii) Two distinct lines at the most intersect at one point.

Question 3:

(i) Given two points P and Q. Find how many line segments do they determine.

(ii) Name the line segments determined by the three collinear points P, Q and R.

Solution:

(i) One line segment is incident on the points P and Q.

(ii) PQ, QR, PR are line segments determined by the three collinear points P, Q and R.

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, namely,  AB, CD, AC, PQ and DS respectively.

(ii) Five rays : PA, RB, DC, QS, DS

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

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

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.