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#### Page No 166:

#### Question 1:

Name all the line segments in each of the following figures:

(i) Figure

(ii) Figure

(iii) Figure

#### Answer:

(i) The line segments are:

$\overline{YX}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsYandX.\phantom{\rule{0ex}{0ex}}\overline{YZ}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsYanZ.$

(ii)

$\overline{AD}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsAandD.\phantom{\rule{0ex}{0ex}}\overline{AB}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsAandB.\phantom{\rule{0ex}{0ex}}\overline{AC}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsAandC.\phantom{\rule{0ex}{0ex}}\overline{AE}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsAandE.\phantom{\rule{0ex}{0ex}}\overline{DB}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsBandD.\phantom{\rule{0ex}{0ex}}\overline{BC}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsBandC.\phantom{\rule{0ex}{0ex}}\overline{CE}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsCandE.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}$

(iii)

$\overline{PS}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsPandS.\phantom{\rule{0ex}{0ex}}\overline{PQ}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsPandQ.\phantom{\rule{0ex}{0ex}}\overline{QR}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsQandR.\phantom{\rule{0ex}{0ex}}\overline{RS}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsRandS.\phantom{\rule{0ex}{0ex}}\overline{PR}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsPandR.\phantom{\rule{0ex}{0ex}}\overline{QS}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsQandS.$

#### Page No 166:

#### Question 2:

Identify and name the line segments and rays in each of the following figures:

(i) Figure

(ii) Figure

(iii) Figure

#### Answer:

(i) Line segment is $\overline{AB}.ThisisbecauseithastwoendpointsAandB.$

Rays are:

$\underset{AC}{\to}\phantom{\rule{0ex}{0ex}}ThisisbecauseithasonlyoneendpointA.\phantom{\rule{0ex}{0ex}}\underset{BD}{\to}\phantom{\rule{0ex}{0ex}}ThisisbecauseithasonlyoneendpointB.$

(ii) Line segments are:

$\overline{EP}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsEandP.\phantom{\rule{0ex}{0ex}}\overline{EG}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsEandG.\phantom{\rule{0ex}{0ex}}\overline{GP}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsGandP.$

Rays are:

$\overrightarrow{EF}\phantom{\rule{0ex}{0ex}}Thisisbecauseithasonlyoneendpoint,i.e.E.\phantom{\rule{0ex}{0ex}}\overrightarrow{GH}\phantom{\rule{0ex}{0ex}}Thisisbecauseithasonlyoneendpoint,i.e.G.\phantom{\rule{0ex}{0ex}}\overrightarrow{PQ}\phantom{\rule{0ex}{0ex}}Thisisbecauseithasonlyoneendpoint,i.e.P.\phantom{\rule{0ex}{0ex}}$

(iii) Line segments are:

$\overline{OL}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsOandL.\phantom{\rule{0ex}{0ex}}\overline{OP}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsOandP.$

Rays are:

$\overrightarrow{LM}\phantom{\rule{0ex}{0ex}}Thisisbecauseithasonlyoneendpoint,i.e.L.\phantom{\rule{0ex}{0ex}}\overrightarrow{PQ}\phantom{\rule{0ex}{0ex}}Thisisbecauseithasonlyoneendpoint,i.e.P.$

#### Page No 167:

#### Question 3:

In the adjoining figure, name

(i) four line segments;

(ii) four rays;

(iii) two non-intersecting line segments.

Figure

#### Answer:

(i)

$\overline{PR}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsPandR.\phantom{\rule{0ex}{0ex}}\overline{QS}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsQandS.\phantom{\rule{0ex}{0ex}}\overline{PQ}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsPandQ.\phantom{\rule{0ex}{0ex}}\overline{RS}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsRandS.$

(ii)

$\overrightarrow{PA}\phantom{\rule{0ex}{0ex}}Thisisbecauseithasonlyoneendpoint,i.e.P.\phantom{\rule{0ex}{0ex}}\overrightarrow{RB}\phantom{\rule{0ex}{0ex}}Thisisbecauseithasonlyoneendpoint,i.e.R.\phantom{\rule{0ex}{0ex}}\overrightarrow{QC}\phantom{\rule{0ex}{0ex}}Thisisbecauseithasonlyoneendpoint,i.e.Q.\phantom{\rule{0ex}{0ex}}\overrightarrow{SD}\phantom{\rule{0ex}{0ex}}Thisisbecauseithasonlyoneendpoint,i.e.S.$

(iii)

$\overline{PR}and\overline{QS}arethetwonon-intersectinglinesegmentsastheydonothaveanypointincommon.$

#### Page No 167:

#### Question 4:

What do you mean by collinear points?

(i) How many lines can you draw passing through three collinear points?

(ii) Given three collinear points *A*, *B*, *C*. How many line segments do they determine? Name them.

Figure

#### Answer:

__ COLLINEAR POINTS : __

Three or more points in a plane are said to be collinear if they all lie in the same line. This line is called the line of collinearity for the given points.

(i) We can draw only one line passing through three collinear points.

(ii) 3 Line segments are:

$\overline{AB}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsAandB.\phantom{\rule{0ex}{0ex}}\overline{BC}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsBandC.\phantom{\rule{0ex}{0ex}}\overline{AC}\phantom{\rule{0ex}{0ex}}ThisisbecauseithastwoendpointsAandC.$

#### Page No 167:

#### Question 5:

In the adjoining figure, name:

(i) four pairs of intersecting lines

(ii) four collinear points

(iii) three noncollinear points

(iv) three concurrent lines

(v) three lines whose point of intersection is *P*

Figure

#### Answer:

(i)

$\overleftrightarrow{PS}and\overleftrightarrow{AB}intersectingatS.\phantom{\rule{0ex}{0ex}}\overleftrightarrow{CD}and\overleftrightarrow{RS}intersectingatR.\phantom{\rule{0ex}{0ex}}\overleftrightarrow{PS}and\overleftrightarrow{CD}intersectingatP.\phantom{\rule{0ex}{0ex}}\overleftrightarrow{AB}and\overleftrightarrow{RS}intersectingatS.$

(ii) A, Q, S and B are four collinear points as they all lie on the same line $\overleftrightarrow{AB}$.

(iii) A, C and B are non-collinear points as they do not lie on the same line.

(iv)

$\overleftrightarrow{PS},\overleftrightarrow{RS}and\overleftrightarrow{AB}arethreeconcurrentlinespas\mathrm{sin}gthroughthesamepointS$.

(v)

$\overleftrightarrow{PS},\overleftrightarrow{PQ}and\overleftrightarrow{CD}havecommonpointofintersectionP$.

#### Page No 167:

#### Question 6:

Mark three noncollinear points *A*, *B*, *C*, as shown. Draw lines through these points taking two at a time. Name the lines. How many such different lines can be drawn?

Figure

#### Answer:

Taking points A and B, we can draw only one line $\overleftrightarrow{AB}$.

Taking points B and C, we can draw only one line $\overleftrightarrow{BC}\phantom{\rule{0ex}{0ex}}$.

Taking points A and C, we can draw only one line $\overleftrightarrow{AC}$.

We can draw only three lines through these non-collinear points A ,B and C.

#### Page No 167:

#### Question 7:

Count the number of line segments drawn in each of the following figures and name them.

(i) Figure

(ii) Figure

(iii) Figure

(iv) Figure

#### Answer:

(i) There are 6 line segments. These are:

$\overline{AB}(withendpointsAandB)\phantom{\rule{0ex}{0ex}}\overline{AC}(withendpointsAandC)\phantom{\rule{0ex}{0ex}}\overline{AD}(withendpointsAandD)\phantom{\rule{0ex}{0ex}}\overline{BC}(withendpointsBandC)\phantom{\rule{0ex}{0ex}}\overline{BD}(withendpointsBandD)\phantom{\rule{0ex}{0ex}}\overline{CD}(withendpointsCandD)\phantom{\rule{0ex}{0ex}}$

(ii) There are 10 line segments. These are:

$\overline{AB}(withendpointsAandB)\phantom{\rule{0ex}{0ex}}\overline{BC}(withendpointsBandC)\phantom{\rule{0ex}{0ex}}\overline{CD}(withendpointsCandD)\phantom{\rule{0ex}{0ex}}\overline{AD}(withendpointsAandD)\phantom{\rule{0ex}{0ex}}\overline{AC}(withendpointsAancC)\phantom{\rule{0ex}{0ex}}\overline{BD}(withendpointsBandD)\phantom{\rule{0ex}{0ex}}\overline{AO}(withendpointsAandO)\phantom{\rule{0ex}{0ex}}\overline{CO}(withendpointsCandO)\phantom{\rule{0ex}{0ex}}\overline{BO}(withendpointsBandO)\phantom{\rule{0ex}{0ex}}\overline{DO}(withendpointsDandO)\phantom{\rule{0ex}{0ex}}$

(iii) There are 6 line segments. They are:

$\overline{AB},\overline{AF},\overline{FB},\phantom{\rule{0ex}{0ex}}\overline{EC},\overline{ED},\overline{DC}\phantom{\rule{0ex}{0ex}}$

(iv) There are 12 line segments. They are:

$\overline{AB},\overline{AD},\overline{AE}\phantom{\rule{0ex}{0ex}}\overline{BC},\overline{BF}\phantom{\rule{0ex}{0ex}}\overline{CG},\overline{CD}\phantom{\rule{0ex}{0ex}}\overline{HG},\overline{HE},\overline{DH}\phantom{\rule{0ex}{0ex}}\overline{EF},\overline{GF}\phantom{\rule{0ex}{0ex}}$

#### Page No 167:

#### Question 8:

Consider the line $\overleftrightarrow{PQ}$ given below and find whether the given statements are true or false:

(i) *M* Is a point on ray $\overrightarrow{NQ}$.

(ii) *L* is a point on ray $\overrightarrow{MP}$.

(iii) Ray $\overrightarrow{MQ}$ is different from ray $\overrightarrow{NQ}$.

(iv) *L*, *M*, *N* are points on line segment $\overline{LN}$.

(v) Ray $\overrightarrow{LP}$ is different from ray $\overrightarrow{LQ}$.

Figure

#### Answer:

(i) False

M is outside ray NQ.

(ii) True

L is placed between M and P.

(iii) True

Ray MQ is extended endlessly from M to Q and ray NQ is extended endlessly from N to Q.

(iv) True

(v) True

$\overrightarrow{LP}isextendedendlesslyfromLtoP.\phantom{\rule{0ex}{0ex}}\overrightarrow{LQ}isextendedendlesslyfromLtoQ.$

#### Page No 168:

#### Question 9:

Write 'T' for true and 'F' for false in case of each of the following statements:

(i) Every point has a size.

(ii) A line segment has no length.

(iii) Every ray has a finite length.

(iv) The ray $\overrightarrow{AB}$ is the same as the ray $\overrightarrow{BA}$.

(v) The line segment $\overline{AB}$ is the same as the line segment $\overline{BA}$.

(vi) The line $\overleftrightarrow{AB}$ is the same as the line $\overleftrightarrow{BA}$.

(vii) Two points *A* and *B* in a plane determine a unique line segment.

(viii) Two intersecting lines intersect at a point.

(ix) Two intersecting planes intersect at a point.

(x) If points *A*, *B*, *C* are collinear and points *C*, *D*, *E* are collineaer then the pints *A*,*B*, *C*, *D*, *E* are collinear.

(xi) One and only one ray can be drawn with a given end point.

(xii) One and only one line can be drawn to pass through two given points.

(xiii) An unlimited number of lines can be drawn to pass through a given point.

#### Answer:

(i) False

A point does not have any length, breadth or thickness.

(ii) False

A line segment has a definite length.

(iii) False

A ray has no definite length.

(iv) False

Ray AB has initial point A and is extended endlessly towards B, while ray BA has initial point B and is extended endlessly towards A.

(v) True

This is because both the line segments have definite length with end points A and B.

(vi) True

This is because it neither has a definite length nor any end point.

(vii) True

Only one line segment can pass through the two given points.

(viii) True

(ix) False

Two intersecting planes intersect at a line.

(x) False

Different set of collinear points need not be collinear.

(xi) False

With point P, endless rays (like PA, PB, PC, PD, PE, PF) can be drawn.

(xii) True

Two points define one unique line.

(xiii) True

#### Page No 168:

#### Question 10:

Fill in the blanks:

(i) A line segment has a .............. length.

(ii) A ray has .............. end point.

(iii) A line has .............. end point.

(iv) A ray has no .............. length.

(v) A line .............. be drawn on a paper.

#### Answer:

(i) definite

(ii) one

(iii) no

(iv) definite

(v) cannot

#### Page No 168:

#### Question 1:

Which of the following has no end points?

(a) A line segment

(b) A ray

(c) A line

(d) None of these

#### Answer:

(c) A line does not have any end point. It is a line segment that is extended endlessly on both sides.

#### Page No 168:

#### Question 2:

Which of the following has one end point?

(a) A line

(b) A ray

(c) A line segment

(d) None of these

#### Answer:

(b) A ray has one end point, which is called the initial point. It is extended endlessly towards the other direction.

#### Page No 168:

#### Question 3:

Which of the following has two end points?

(a) A line segment

(b) A ray

(c) A line

(d) None of these

#### Answer:

(a) A line segment has two end points and a definite length that can be measured.

#### Page No 168:

#### Question 4:

Which of the following has definite length?

(a) A line

(b) A line segment

(c) A ray

(d) None of these

#### Answer:

(b) A line segment has a definite length that can be measured by a ruler and, therefore, it can be drawn on a paper.

#### Page No 168:

#### Question 5:

Which of the following can be drawn on a piece of paper?

(a) A line

(b) A line segment

(c) A ray

(d) A plane

#### Answer:

(b) A line segment has a definite length that can be measured by a ruler. So, it can be drawn on a paper.

#### Page No 168:

#### Question 6:

How many lines can be drawn passing through a given point?

(a) One only

(b) Two

(c) Three

(d) Unlimited number

#### Answer:

(d) Unlimited number of lines can be drawn.

#### Page No 168:

#### Question 7:

How many lines can be drawn passing through two given point?

(a) One only

(b) Two

(c) Three

(d) Unlimited number

#### Answer:

(a) Only one line can be drawn that passes through two given points.

#### Page No 168:

#### Question 8:

Two planes intersect

(a) at a point

(b) in a plane

(c) in a line

(d) none of these

#### Answer:

(c) Two intersecting planes intersect in a line.

#### Page No 168:

#### Question 9:

Two lines intersect

(a) at a point

(b) at two points

(c) at an infinite number of points

(d) in a line

#### Answer:

(a) Two lines intersect at a point.

#### Page No 169:

#### Question 10:

Two points in a plane determine

(a) exactly one line segment

(b) exactly two line segments

(c) an infinite number of line segments

(d) none of these

#### Answer:

(a) exactly one line segment

Two points in a plane determine exactly one line segment with those two points as its end points.

#### Page No 169:

#### Question 11:

The minimum number of points of intersection of three lines in a plane is

(a) 1

(b) 2

(c) 3

(d) 0

#### Answer:

(d) 0

Three lines will not necessarily intersect in a plane. Thus, the minimum point of intersection will be 0.

#### Page No 169:

#### Question 12:

The maximum number of points of intersection of three lines in a plane is

(a) 0

(b) 1

(c) 2

(d) 3

#### Answer:

(d) 3

The maximum number of points of intersection of three lines that intersect in a plane are three.

#### Page No 169:

#### Question 13:

Choose the correct statement:

(a) every line has a definite length

(b) every ray has a definite length

(c) every line segment has a definite length

(d) none of these

#### Answer:

(c) Every line segment has a definite length.

Every line segment has a definite length, which can be measured using a ruler.

#### Page No 169:

#### Question 14:

Choose the false statement:

(a) Line $\overleftrightarrow{AB}$ is the same as line $\overleftrightarrow{BA}$

(b) Ray $\overrightarrow{AB}$ is the same as ray $\overrightarrow{BA}$

(c) Line segment $\overline{AB}$ is the same as teh line segment $\overline{BA}$

(d) None of these

#### Answer:

(b) Ray $\overrightarrow{\mathrm{AB}}\mathrm{is}\mathrm{same}\mathrm{as}\mathrm{ray}\overrightarrow{\mathrm{BA}}$

This is because the initial points in these rays are A and B, respectively, and are extended endlessly towards B and A, respectively.

#### Page No 169:

#### Question 15:

How many rays can be drawn with a given point as the initial point?

(a) One

(b) Two

(c) An unlimited number

(d) A limited number only

#### Answer:

(c) An unlimited number of rays can be drawn with a given point as the initial point. For example:

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