## RD Sharma Solutions Class 9 Chapter 7 Ex 7.1

*1) Define the following terms.*

*(i) Â Line segment Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (v) Concurrent lines *

*(ii) Collinear pointsÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (vi) Ray*

*(iii) Parallel linesÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (vii) Half-line*

*(iv) Intersecting lines*

**Solution**

(i) __Line-segment__:

Give two points A and B on a line I. the connected part (segment) of the line with end points at A and B is called the line segment AB.

(ii) __Collinear points__:

Three or more points are said to be collinear if there is a line which contains all of them.

(iii) __Parallel lines__:

Two lines l and m in a plane are said to be parallel lines if they do not intersect each other.

(iv) __Intersecting lines__:

Two lines are intersecting if they have a common point. The common point is called point of intersection.

(v) __Concurrent lines__:

Three or more lines are said to be concurrent if there is a point which lies on all of them.

(vi) __Ray__:

A line in which one end point is fixed and the other part can be extended endlessly.

(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 half-line.

*2) (i) How many lines can pan through a given point? *

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

**Solution**

(i) Infinitely many

(ii) One

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

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

**Solution**

(i) One

(ii) PQ, QR, PR

*Â *

*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 *

**Â **

**Solution **

(i) False Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (vi) True

(ii) False Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (vii) False

(iii) False Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (viii) False

(iv) TrueÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (ix) False

(v) FalseÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (x) False

*5) In the below figure. Name the following:*

*Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â *

*Â ***Solution: **

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

(ii) Five rays \(\underset{PA}{\rightarrow},\;\underset{RB}{\rightarrow},\;\underset{DC}{\rightarrow},\;\underset{QS}{\rightarrow},\;\underset{DS}{\rightarrow}\)

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

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

*Â *

*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.