2 Marks Questions

Question 12 Marks

In Fig.,
$a.\ $What is $AE + EC?$
$b.\ $What is $AC - EC?$
$c.\ $What is $BD - BE?$
$d.\ $What is $BD - DE?$

Answer

From the figure, we observe that:
$a.\ AE + EC = AC$
$b.\ AC - EC = AE$
$c.\ BD - BE = ED$
$d.\ BD - DE = BE$

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Question 22 Marks

State the mid points of all the sides of Fig.

Answer

Mid-point of a line segment divides it into two equal parts.
Clearly, from the figure, $AZ = ZB, AX = XC$ and $CY = YB.$
So $Z, X$ and $Y$ are the mid-points of $AS, AC$ and $CB,$
respectively. Hence, there are $3$ mid-points, i.e. $X, Z$ and $Y.$

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Question 32 Marks

In Fig.,
$a.\ $Is $AC + CB = AB?$
$b.\ $Is $AB + AC = CB?$
$c.\ $Is $ AB + BC = CA?$

Answer

$a.\ $Yes.
$b.\ $No, it is not possible.
$c.\ $No, it is not possible.

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Question 42 Marks

Look at Fig. Mark a point:
$1.A$ which is in the interior of both $\angle1$ and $\angle2$
$2.B$ which is in the interior of only $\angle1$
$3.$oint $C$ in the interior of $\angle1.$

Now, state whether points $B$ and $C$ lie in the interior of $\angle2$ also.

Answer

Yes, points $B$ and $C$ lie in the interior of $\angle 2$ also. Since, $\angle 1$ is in interior of $\angle 2, $ then all the points lying inside the $\angle1$, will also lie inside the $\angle2$

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Question 52 Marks

How many lines can be drawn which are perpendicular to a given line and pass through a given point lying outside it?

Answer

Perpendicular line from a given point to a given line is the shortest distance between them. Only one shortest distance is possible. Thus, only one perpendicular line is possible from the given point (outside the line) to a given line.

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Question 62 Marks

Construct the following angles using set-squares: $60^\circ $

Answer

$60^\circ $ Place $30^\circ $ set-square as shown in the figure. Draw the rays $BA$ and $BC$ along the edges from the vertex of $60^\circ $ The angle so formed is $60^\circ $
$\angle\text{ABC}=60^{\circ}$

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Question 72 Marks

Construct the following angles using set-squares: $90^\circ $

Answer

$90^\circ $ Place $= 90^\circ $ set-square as shown in the figure. Draw two rays $BC$ and $BA$ along the edges from the vertex of $90^\circ $ angle. The angle so formed is $90^\circ $ angle. $\angle\text{ABC}=90^{\circ}$

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Question 82 Marks

Draw any circle and mark points $A, B$ and $C$ such that:
$1.A$ is on the circle.
$2.B$ is in the interior of the circle.
$3.C$ is in the exterior of the circle.

Answer

We may draw a circle and three required points $A, B, C$ as following-

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Question 92 Marks

Which points in Fig., appear to be mid-points of the line segments? When you locate a mid-point, name the two equal line segments formed by it.

Answer

In figure $(ii),$ point $O$ appears to be the mid-point and equal line segments formed are $OA$ and $OB.$ Also, in figure $(iii),$ point $D$ appears to be the mid-point and equal line segments formed are $BD$ and $DC.$

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Question 102 Marks

How many lines can be drawn to pass through: A given point.

Answer

We can draw infinite number of lines passing through a given point.

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Question 112 Marks

In Fig.,
$a.$ Name any four angles that appear to be acute angles.
$b.$ Name any two angles that appear to be obtuse angles.

Answer

$1.$ The four angles that appear to be acute angles are $\angle\text{AEB}, \angle\text{ADE}, \angle\text{BAE}$ and $\angle\text{BCE}$
$2.$ $\angle\text{BCD}$ and $\angle\text{BAD}$ are angles that appear to be obtuse angles $($answer may vary$).$

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Question 122 Marks

Construct the following angles using set-squares: $45^\circ $

Answer

$45^\circ$ Place $45^\circ$ set-square. Draw two rays $AB$ and $AC$ along the edges from the vertex from the vertex of $45^\circ$ angle of the set- square. The angle so formed is a $45^\circ$ angle. $\angle\text{BAC}=45^{\circ}$

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Question 132 Marks

Using a pair of compasses construct the following angles: $120^\circ $

Answer

Only one line can be drawn with two given points.

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Question 142 Marks

Is it possible for the same:
$a.\ $Line segment to have two different lengths?
$b.\ $Angle to have two different measures?

Answer

$a.\ $No, it is not possible that the same line segments have two different lengths,
$b.\ $No, it is not possible that the same angles have two different measures.

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Question 152 Marks

How many lines can be drawn which are perpendicular to a given line and pass through a given point lying on it?

Answer

At any point on the line, we can draw only one perpendicular line. Thus, on the given line on a point, we can draw only one perpendicular line.

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Question 162 Marks

Can we have two obtuse angles whose sum is:
$a.\ $A reflex angle? Why or why not?
$b.\ $A complete angle? Why or why not?

Answer

$a.\ $Yes, the sum of two obtuse angles is always greater than $180^\circ .$ Hence, the sum of two obtuse angles may be a reflex angle.
$b.\ $No, the sum of two obtuse angles cannot be $360^\circ .$ Because each obtuse angle lies between $90^\circ $ to $180^\circ .$ So, the sum of the two obtuse angles lies between $180^\circ $ to $360^\circ .$

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Question 172 Marks

Mark two points, $A$ and $B$ on a piece of paper and join them. Measure this length. For each of the following draw a line segment $CD$ that is: Equal to the segment $AB.$

Answer

Mark two points, $A$ and $B$ on a piece of paper and join them as follows:

To measure the length of $AB,$ place the ruler with its edge along $AB,$ such that the zero mark of the \ cm side of the ruler coincides with point $A,$ as shown in the figure. Now, read the mark on the ruler, which corresponds to the point $B.$ The reading on the ruler at point $B$ is the length of the line segment $AB.$ Here, $AB = 5.6\ cm$ To draw the line segment $CD$ equal to $AB,$ take a divider and open it, such that the end-point of one of its arms is at $A$ and the end-point of the second arm is at $B,$ as shown in the figure. Then, lift the divider and without disturbing its opening, place the end-points of both hands on the paper, where we have to draw $CD$.

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Question 182 Marks

How many rays are represented in Fig.? Name them.

Answer

We know that a ray has fixed starting point and it can be drawn to infinity. If we take $0$ as starting point, we will have a ray in every given direction. So, our rays are, $\overrightarrow{\text{OA}},\overrightarrow{\text{OB}},\overrightarrow{\text{OC}},\overrightarrow{\text{OD}},\overrightarrow{\text{OE}},\overrightarrow{\text{OF}},\overrightarrow{\text{OG}},\overrightarrow{\text{OH}}.$ Thus, the number of rays in the figure is 8.

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Question 192 Marks

Given a line $BC$ and a point $A$ on it, construct a ray $AD$ using set squares so that $\angle\text{DAC}$ is: $30^\circ$

Answer

Draw a line $BC$ and take a point $A$ on it. Place $30^\circ $ set-square on the line $BC$ such that its vertex of $30^\circ$ angle lies on point $A$ and one edge coincides with the ray $AB$ as shown in figure. Draw the ray $AD.$

Thus $\angle\text{DAC}$ is the required angle of $30^\circ$.

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Question 202 Marks

Using a pair of compasses construct the following angles: $90^\circ $

Answer

We can draw one line with three given points if all the three point are collinear. But, if the points are not collinear, then we cannot draw any line passing through the points.

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