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:
$a.\ \text{AE + EC = AC}$
$b.\ \text{AC - EC = AE}$
$c.\ \text{BD - BE = ED}$
$d.\ \text{BD - DE = BE}$

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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 $\angle1$
$3.$ Point $C$ 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 $\angle2$ also. Since, $\angle1$ is in interior of $\angle2, $ then all the points lying inside the $\angle1$, will also lie inside the $\angle2$

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Question 52 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 62 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 72 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 82 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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