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#### Page No 166:

#### 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:

#### 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:

#### 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:

#### 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:

#### 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:

#### 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:

#### 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:

#### 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:

#### 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:

#### Answer:

(i) definite

(ii) one

(iii) no

(iv) definite

(v) cannot

#### Page No 168:

#### 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:

#### 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:

#### Answer:

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

#### Page No 168:

#### 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:

#### 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:

#### Answer:

(d) Unlimited number of lines can be drawn.

#### Page No 168:

#### Answer:

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

#### Page No 168:

#### Answer:

(c) Two intersecting planes intersect in a line.

#### Page No 168:

#### Answer:

(a) Two lines intersect at a point.

#### Page No 169:

#### 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:

#### Answer:

(d) 0

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

#### Page No 169:

#### Answer:

(d) 3

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

#### Page No 169:

#### 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:

#### 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:

#### Answer:

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

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