Question 11 Mark
Many lines can pass through two given points.
Answer
View full question & answer→Only one line can pass through two given points.
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Question 21 Mark
An angle greater than $180^\circ $ and less than a complete angle is called _______.
Answer
View full question & answer→An angle greater than $180^\circ $ and less than a complete angle is called Reflex Angle.
Question 31 Mark
How many line segments are there in Fig.?
Answer
View full question & answer→There is only one line segment $AB.$
Question 41 Mark
The number of diagonals in a hexagon is ________.
Answer
View full question & answer→The number of diagonals in a hexagon is $9.$
Solution: Number of sides in hexagon $(n) = 6$
Number of diagonals $=\frac{\text{n}(\text{n}-3)}{2}=\frac{6(6-3)}{2}=9$
Solution: Number of sides in hexagon $(n) = 6$
Number of diagonals $=\frac{\text{n}(\text{n}-3)}{2}=\frac{6(6-3)}{2}=9$
Question 51 Mark
In Fig. $2.15,$ points $A, B, C, D$ and $E$ are collinear such that $AB = BC = CD = DE.$ Then,
$a.\ AD = AB + ......$
$b.\ AD = AC + ......$
$c.$ Mid point of $AE$ is $......$
$d.$ Mid point of $CE$ is $......$
$e.\ AE = $......$ \times AB.$
$a.\ AD = AB + ......$
$b.\ AD = AC + ......$
$c.$ Mid point of $AE$ is $......$
$d.$ Mid point of $CE$ is $......$
$e.\ AE = $......$ \times AB.$
Answer
View full question & answer→$a.\ AD = AB+ BC + CD = AB + BD$
$b.\ AD = AB + BC + CD = AC + CD$
$e.\ AE = AB + BC + CD + DE$ $AE = AB + AB + AB + AB$
$AE = 4 AS$
$b.\ AD = AB + BC + CD = AC + CD$
$c.$ Given, $AB = BC =CD = DE$
$\therefore\text{AE}=\text{AC}+\text{CE}$ So, $C$ is the mid-point of $AE.$
$d.$ Given, $AB = BC = CD = DE$ $CE = CD + DE$ So, $D$ is the mid-point of $CE.$$\therefore\text{AE}=\text{AC}+\text{CE}$ So, $C$ is the mid-point of $AE.$
$e.\ AE = AB + BC + CD + DE$ $AE = AB + AB + AB + AB$
$AE = 4 AS$
Question 61 Mark
The number of common points in the two angles marked in ______ .
Answer
View full question & answer→The number of common points in the two angles marked in $3.$
Solution:
The common points in $\angle\text{DEF}$ and $\angle\text{BAC}$ are $P, 0$ and $R.$
Solution:
The common points in $\angle\text{DEF}$ and $\angle\text{BAC}$ are $P, 0$ and $R.$
Question 71 Mark
If two rays intersect, will their point of intersection be the vertex of an angle of which the rays are the two sides?
Answer
View full question & answer→No, because angle is made when two rays intersect at common point. The common point is known as vertex of an angle.
Question 81 Mark
Name the vertices and the line segments in Fig.
Answer
View full question & answer→There are five vertices in the given figure, namely $A, B, C, D$ and $E$ and there are seven line segments in the given figure, namely $AS, SC, CD, DE, EA, AC$ and $AD.$
Question 91 Mark
Using the information given, name the right angles in Fig. $\text{RT}\bot\text{ST}$ 
Answer
View full question & answer→$\angle\text{RTS}\because\text{RT}\bot\text{ST}$
Question 101 Mark
Name all the line segments in Fig.
Answer
View full question & answer→A line segment is a part of line having finite length. Hence, all the line segments shown in the figure are $AB, AC, AD, AE, BC, BD, BE, CD, CE$ and $DE.$
Question 111 Mark
Using the information given, name the right angles of Figure: $\text{RS}\bot\text{RW}$ 
Answer
View full question & answer→$\angle\text{RTW}$ and $\angle\text{RTS}$ because $\text{RT}\bot\text{SW}$
Question 121 Mark
What conclusion can be drawn from Figure, if: $BD$ bisects $\angle\text{ABC?}$
Answer
View full question & answer→If $BD$ bisects $\angle\text{ABC,}$ then $\angle\text{ABD}=\angle\text{CBD.}$
Because an angle bisector bisects an angle into two equal angles.
Because an angle bisector bisects an angle into two equal angles.
Question 131 Mark
If the arms of an angle on the paper are increased, the angle increases.
Answer
View full question & answer→If the size of the arms changes, then there will be no change in the measure of the angle formed by those arms.
Question 141 Mark
Two angles can have exactly five points in common.
Answer
View full question & answer→Two angles can have either one or two points in common.
Question 151 Mark
What is common in the following figures $(i)$ and $(ii)$ Fig.$?$
Is Fig. $(i)$ that of triangle$?$ if not, why$?$
Is Fig. $(i)$ that of triangle$?$ if not, why$?$
Answer
View full question & answer→Both the figures have three line segments.
Figure $(i)$ is not a triangle because it is not a closed figure.
Figure $(i)$ is not a triangle because it is not a closed figure.
Question 161 Mark
Measures of $\angle\text{ABC}$ and $\angle\text{CBA}$ in Fig. are the same.
Answer
View full question & answer→Because in both measurements $\angle\text{ABC}$ and $\angle\text{CBA,}$ the common angle is $B \angle\text{ABC} = \angle\text{CBA}$
Question 171 Mark
In Figure: 
$a.\ \angle\text{AOD}$ is a/ an $.....$ angle.
$b.\ \angle\text{COA}$ is a/ an $.....$ angle.
$c.\ \angle\text{AOE}$ is a/ an $.....$ angle.
$a.\ \angle\text{AOD}$ is a/ an $.....$ angle.
$b.\ \angle\text{COA}$ is a/ an $.....$ angle.
$c.\ \angle\text{AOE}$ is a/ an $.....$ angle.
Answer
$c.\ \angle\text{AOE}$ is a/ an obtuse angle.
Solution:
$a.$ Since, $\angle\text{AOD}=\angle\text{AOB}+\angle\text{BOC}+\angle\text{COD}=30^\circ+20^\circ+40^\circ=90^\circ$
So, $\angle\text{AOD}=90^\circ$ is a right angle.
$b.$Since, $\angle\text{COA}=\angle\text{COB}+\angle\text{BOA}=20^\circ+30^\circ=50^\circ$ Because $\angle\text{COA}=50^\circ<90^\circ.$
So, $\angle\text{COA}$ is an acute angle.
$c.$Since, $\angle\text{AOE}=\angle\text{AOB}+\angle\text{BOC}+\angle\text{COD}+\angle\text{DOE},$
$=30^\circ+20^\circ+40^\circ+40^\circ=130^\circ$
Because $\angle\text{AOE}=130^\circ>90^\circ$ So, $\angle\text{AOE}$ is an obtuse angle.
View full question & answer→$a.\ \angle\text{AOD}$ is a/ an right angle.
$b.\ \angle\text{COA}$ is a/ an acute angle.$c.\ \angle\text{AOE}$ is a/ an obtuse angle.
Solution:
$a.$ Since, $\angle\text{AOD}=\angle\text{AOB}+\angle\text{BOC}+\angle\text{COD}=30^\circ+20^\circ+40^\circ=90^\circ$
So, $\angle\text{AOD}=90^\circ$ is a right angle.
$b.$Since, $\angle\text{COA}=\angle\text{COB}+\angle\text{BOA}=20^\circ+30^\circ=50^\circ$ Because $\angle\text{COA}=50^\circ<90^\circ.$
So, $\angle\text{COA}$ is an acute angle.
$c.$Since, $\angle\text{AOE}=\angle\text{AOB}+\angle\text{BOC}+\angle\text{COD}+\angle\text{DOE},$
$=30^\circ+20^\circ+40^\circ+40^\circ=130^\circ$
Because $\angle\text{AOE}=130^\circ>90^\circ$ So, $\angle\text{AOE}$ is an obtuse angle.
Question 181 Mark
Find out the incorrect statement, if any, in the following:
An angle is formed when we have:
$a.$ Two rays with a common end$-$point.
$b.$ Two line segments with a common end$-$point.
$c.$ A ray and a line segment with a common end$-$point.
An angle is formed when we have:
$a.$ Two rays with a common end$-$point.
$b.$ Two line segments with a common end$-$point.
$c.$ A ray and a line segment with a common end$-$point.
Answer
View full question & answer→Angle is made by two rays or lines having a common end point. So, options $(b)$ and $(c)$ are incorrect.
Question 191 Mark
In Fig. Points lying in the interior of the triangle $PQR$ are ______, that in the exterior are ______ and that on the triangle itself are ______.
Answer
View full question & answer→Those points which lie inside the triangle are known as interior points and those lie outside the triangle are known as exterior points. In the given figure, points lying in the interior of $\triangle\text{PQR}$ are $O$ and $S.$ Points lying in the exterior of $\triangle\text{PQR}$ are $N$ and $T.$ Points lying on the $\triangle\text{PQR}$ is $M, P, Q$ and $R.$
Question 201 Mark
Write down fifteen angles $($less than $180^\circ )$ involved in Fig.
Answer
View full question & answer→The fifteen angles $($less than $180^\circ )$ shown in the figure are:
$\angle\text{EAD}, \angle\text{AEF}, \angle\text{EFD}, \angle\text{ADF}, \angle\text{DFC}, \angle\text{DCF}, \text{CDF}, $
$\angle\text{BEF}, \angle\text{BFE}, \angle\text{EBF}, \angle\text{FBC},\angle\text{FCB}, \angle\text{BFC}, \angle\text{ABC}$ and $\angle\text{ACS}$
$\angle\text{EAD}, \angle\text{AEF}, \angle\text{EFD}, \angle\text{ADF}, \angle\text{DFC}, \angle\text{DCF}, \text{CDF}, $
$\angle\text{BEF}, \angle\text{BFE}, \angle\text{EBF}, \angle\text{FBC},\angle\text{FCB}, \angle\text{BFC}, \angle\text{ABC}$ and $\angle\text{ACS}$
Question 211 Mark
Two parallel lines meet each other at some point.
Answer
View full question & answer→By definition, parallel lines are those which never intersect each other.
Question 221 Mark
What conclusion can be drawn from Figure, if:
$DB$ is the bisector of $\angle\text{ADC}?$
$DB$ is the bisector of $\angle\text{ADC}?$
Answer
View full question & answer→If $DB$ is the bisector of $\angle\text{ADC,}$
then $\angle\text{ADB}=\angle\text{CDB}$
Because an angle bisector bisects an angle into two equal angles.
then $\angle\text{ADB}=\angle\text{CDB}$
Because an angle bisector bisects an angle into two equal angles.
Question 231 Mark
Using the information given, name the right angles of Figure: $\text{AC}\bot\text{CD}$ 
Answer
View full question & answer→$\angle\text{ACD}$ because $\text{AC}\bot\text{CD}$
Question 241 Mark
In Fig.how many points are marked? Name them.
Answer
View full question & answer→There are four points marked, namely $A, B, C$ and $D.$
Question 251 Mark
What conclusion can be drawn from Figure, if:
$DC$ is the bisector of $\angle\text{ADB}, \text{CA}\bot\text{DA}$ and $\text{CB}\bot\text{DB}?$
$DC$ is the bisector of $\angle\text{ADB}, \text{CA}\bot\text{DA}$ and $\text{CB}\bot\text{DB}?$
Answer
View full question & answer→If $DC$ is the bisector of $\angle\text{ADB,}$
then $\angle\text{ADC} = \angle\text{BDC.}$
Also, $CADA$ and $CBLDB,$
then $\angle\text{CAD}=90^\circ$ and $\angle\text{CBD}=90^\circ$
then $\angle\text{ADC} = \angle\text{BDC.}$
Also, $CADA$ and $CBLDB,$
then $\angle\text{CAD}=90^\circ$ and $\angle\text{CBD}=90^\circ$
Question 261 Mark
How many line segments are there in Fig.? Name them.
Answer
View full question & answer→There are three line segments, namely $AB, BC$ and $AC.$
Question 271 Mark
The number of common points in the two angles marked in Fig. is ______ .
Answer
View full question & answer→The number of common points in the two angles marked in Fig. is $1.$
Solution:
The common point in $\angle\text{BAC}$ and $\angle\text{DAE}$ is $A.$
Solution:
The common point in $\angle\text{BAC}$ and $\angle\text{DAE}$ is $A.$
Question 281 Mark
Two line segments may intersect at two points.
Answer
View full question & answer→Two line segments will intersect each other at only one point.
Question 291 Mark
Will the lengths of line segment $AB$ and line segment $BC$ make the length of line segment $AC$ in Fig.$?$
Answer
View full question & answer→Yes, because the line segments $AB$ and $BC$ together form the line segment $AC.$ i.e.
$AB + BC = AC$
$AB + BC = AC$
Question 301 Mark
If line $PQ ||$ line $m,$ then line segment $PQ || m.$
Answer
View full question & answer→If a line is parallel to another line, then their parts are also parallel.
Question 311 Mark
The number of triangles in Fig. is ______. Their names are ______.
Answer
View full question & answer→$\triangle\text{AOB},\triangle\text{AOC},\triangle\text{COD},\triangle\text{ABC},\triangle\text{ACD}.$
Question 321 Mark
A horizontal line and a vertical line always intersect at right angles.
Answer
View full question & answer→Lines that never slant up or down are called horizontal lines.
Lines that go straight up and down are called vertical lines.
Let $AS$ be a horizontal line and $CD$ be a vertical line, which intersect at $0.$
Clearly, $\angle\text{AOD}, \angle\text{AOC},\angle\text{COB}$ and $\angle\text{BOD}$ are right angles.
Lines that go straight up and down are called vertical lines.
Let $AS$ be a horizontal line and $CD$ be a vertical line, which intersect at $0.$
Clearly, $\angle\text{AOD}, \angle\text{AOC},\angle\text{COB}$ and $\angle\text{BOD}$ are right angles.
Question 331 Mark
If the arms of an angle on the paper are decreased, the angle decreases.
Answer
View full question & answer→If the size of the arms changes, then there will be no change in the measure of the angle formed by those arms.
Question 341 Mark
Using the information given, name the right angles of Figure: $\text{OP}\bot\text{AB}$ 
Answer
View full question & answer→$\angle\text{AKO},\angle\text{AKP},\angle\text{BKO}$ and $\angle\text{BKP}$ because $\text{OP}\bot\text{AB}$ and $E$ is their point of intersection.
Question 351 Mark
Using the information given, name the right angles of Figure:
$\text{BA}\bot\text{BD}$
$\text{BA}\bot\text{BD}$
Answer
View full question & answer→ $\angle\text{ABD}$ because $\text{BA}\bot\text{BD}$
Question 361 Mark
In Fig. how many line segments are there? Name them.
Answer
View full question & answer→There are ten line segments, namely $AB, AD, AE, AC, BD, BE, BC, BC, DE, DC$ and $EC.$
Question 371 Mark
An angle is said to be trisected, if it is divided into three equal parts. If in Fig., $\angle\text{BAC} =\angle\text{CAD} =\angle\text{DAE,}$ how many trisectors are there for $\angle\text{BAE?}$
Answer
View full question & answer→For an angle to be trisected, we need two trisectors.
So, for $\angle\text{BAE,}$ we have two trisectors,
i.e. $AC$ and $AD. $
$AC$ and $AD$ divides the $\angle\text{BAE}$ in three equal angles.
So, for $\angle\text{BAE,}$ we have two trisectors,
i.e. $AC$ and $AD. $
$AC$ and $AD$ divides the $\angle\text{BAE}$ in three equal angles.
Question 381 Mark
The number of straight angles in Fig. is ______.
Answer
View full question & answer→The number of straight angles in Fig. is $4.$
i.e. $L_1, L_2, L_3$ and $L_4$.
i.e. $L_1, L_2, L_3$ and $L_4$.
Question 391 Mark
In Fig., how many points are marked? Name them.
Answer
View full question & answer→There are five points marked, namely $A, B, C, D$ and $E.$
Question 401 Mark
In Fig., how many points are marked? Name them.
Answer
View full question & answer→There are three points marked, namely $A, B$ and $C.$
Question 411 Mark
How many points are marked in Fig.? 
Answer
View full question & answer→There are two points marked, namely $A$ and $B.$
Question 421 Mark
The number of right angles in a straight angle is ______ and that in a complete angle is ______.
Answer
View full question & answer→The number of right angles in a straight angle is $2$ and that in a complete angle is $4.$
Question 431 Mark
Only one line can pass through a given point.
Answer
View full question & answer→Infinitely many lines can pass through a given point.
Question 441 Mark
Will the measure of $\angle\text{ABC}$ and of $\angle\text{CBD}$ make measure of $\angle\text{ABD}$ in Fig.? 
Answer
View full question & answer→Yes, because $\angle\text{ABC}$ and $\angle\text{CBD}$ together form $\angle\text{ABD,}$ i.e. $\angle\text{ABC} + \angle\text{CBD} = \angle\text{ABD}$
Question 451 Mark
A pair of opposite sides of a trapezium are ________.
Answer
View full question & answer→If the quadrilateral has one pair of parallel sides, then it is known as trapezium. Hence, a pair of opposite sides of a trapezium is parallel.
Question 461 Mark
How many edges, faces and vertices are there in a sphere?
Answer
View full question & answer→A sphere does not have any edges, faces and vertices.
Question 471 Mark
The number of common points in the two angles marked in Fig. is _____________ .
Answer
View full question & answer→The number of common points in the two angles marked in Fig. is $4.$
Solution: The common points in $\angle\text{PQR}$ and $\angle\text{BAC}$ are $D, E, F$ and $G.$
Solution: The common points in $\angle\text{PQR}$ and $\angle\text{BAC}$ are $D, E, F$ and $G.$
Question 481 Mark
Using the information given, name the right angles of Figure: $\text{AE}\bot\text{CE}$ 
Answer
View full question & answer→$\angle\text{AEC}$ because $\text{AE}\bot\text{CE}$
Question 491 Mark
Using the information given, name the right angles of Figure: $\text{AC}\bot\text{BD}$ 
Answer
View full question & answer→$\angle\text{ACD}$ and $\angle\text{ACB}$ because $\text{AC}\bot\text{BD}$
Question 501 Mark
Using the information given, name the right angles of Figure: $\text{AC}\bot\text{BD}$
Answer
View full question & answer→$\angle\text{AED},\angle\text{AEB},\angle\text{BEC}$ and $\angle\text{DEC}$ because $\text{AC}\bot\text{BD}$ and $E$ is their point of intersection.
Question 511 Mark
Number of angles less than $180^\circ $ in Fig. is ______ and their names are ______.
Answer
View full question & answer→Number of angles less than $180^\circ $ in Fig. is $12$ and their names are: $\angle\text{OAB},\angle\text{OBA},\angle\text{OAC},\angle\text{OCA},\angle\text{OCD},\angle\text{ODC}$
$\angle\text{AOB},\angle\text{AOC},\angle\text{COD},\angle\text{DOB},\angle\text{BAC},\angle\text{ACD}.$
$\angle\text{AOB},\angle\text{AOC},\angle\text{COD},\angle\text{DOB},\angle\text{BAC},\angle\text{ACD}.$
Question 521 Mark
The common part between the two angles $BAC$ and $DAB$ in Fig is ______ .
Answer
View full question & answer→The common part between the two angles $BAC$ and $DAB$ in Fig is Ray AS.
Solution: Since, the common part between $\angle\text{DAB}$ and $\angle\text{BAC}$ is ray $AB.$
Solution: Since, the common part between $\angle\text{DAB}$ and $\angle\text{BAC}$ is ray $AB.$
Question 531 Mark
In Fig. how many line segments are there? Name them.
Answer
View full question & answer→There are six line segments, namely $AB, AC, AD, BC, BD$ and $CD.$
Question 541 Mark
Name the line segments shown in Fig.'
Answer
View full question & answer→There are five line segments in the given figure, namely $AB, BC, CD, DE$ and $EA.$
Question 551 Mark
The number of common points in the two angles marked in Fig. is ______.
Answer
View full question & answer→The number of common points in the two angles marked in Fig. is $2.$
Solution: The common points in the $\angle\text{PDQ}$ and $\angle\text{PAQ}$ are $P$ and $Q.$
Solution: The common points in the $\angle\text{PDQ}$ and $\angle\text{PAQ}$ are $P$ and $Q.$