True False[1 Marks ]

Question 11 Mark

Write True or False in the following. Give reasons for your answer: A triangle $ABC$ can be constructed in which $\angle\text{B}=105^\circ, \angle\text{C}=90^\circ$ and $AB + BC + AC = 10\ cm.$

Answer

Here, $\angle\text{B}=105^\circ, \angle\text{C}=90^\circ$ and $AB + BC + CA = 10cm$
We know that, sum of angles of a triangle is $180^\circ $
$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
Here, $\angle\text{B}+\angle\text{C}=105^\circ+90^\circ$
$=195^\circ>180^\circ$ which is not true.
Thus, $\triangle\text{ABC}$ with given conditions cannot be constructed.

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Question 21 Mark

Write True or False in the following. Give reasons for your answer: An angle of $52.5^\circ $ can be constructed.

Answer

To construct an angle of $52.5^\circ $ firstly construct an angle of $90^\circ ,$
then construct an angle of $120^\circ $ and then plot an angle bisector of $120^\circ$ and $90^\circ$ to get an angle $105^\circ (90^\circ + 15^\circ ).$
Now, bisect this angle to get an angle of $52.5^\circ $

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Question 31 Mark

Write True or False in the following. Give reasons for your answer: A triangle $ABC$ can be constructed in which $\angle\text{B}=60^\circ, \angle\text{C}=45^\circ$ and $AB + BC + AC = 12\ cm.$

Answer

We know that, sum of angles of a triangle is $180^\circ \angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
Here, $\angle\text{B}+\angle\text{C}=60^\circ+45^\circ=105^\circ<180^\circ$
Thus, $\triangle\text{ABC}$ with given conditions can be constructed.

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Question 41 Mark

Write True or False in the following. Give reasons for your answer: An angle of $42.5^\circ $ can be constructed.

Answer

Since, $42.5^\circ=\frac{1}{4}\times85^\circ$ and $85^\circ $ cannot be constructed by using ruler and compass.
Also $42.5^\circ $ is not the multiple of $3.$
Therefore, an angle of $42.5^\circ $ can not be constructed.

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Question 51 Mark

Write True or False in the following. Give reasons for your answer: A triangle $ABC$ can be constructed in which $AB = 5\ cm,$ $\angle\text{A}=45^\circ$ and $BC + AC = 5\ cm.$

Answer

Here $AB = BC + AC = 5\ cm.$ Since sum of two sides of a triangle is always greater than the third side, so we cannot construct a triangle in which $AB = BC + AC.$

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Question 61 Mark

Write True or False in the following. Give reasons for your answer:
A triangle $ABC$ can be constructed in which $BC = 6\ cm,$ $\angle\text{C}=30^\circ$ and $ AC - AB = 4\ cm.$

Answer

Since difference of two sides of a triangle is always smaller than the third side.
Here, $AC - AB (= 4\ cm) < BC (= 6\ cm).$
Therefore, the given triangle can be constructed and given statement is true.

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Maths True False[1 Marks ]

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