Question 1 :
State true or false:Whether it is possible to construct a triangle or not with its sides equal to $5$&#160;cm, $7$ cm, and $4$ cm<br/>Ans: Yes

Question 4 :
In $\triangle ABC$, $AB=5\ cm, BC= 6\ cm ,AC=4\ cm$. Identify the type of triangle.

Question 5 :
Suppose we have to cover the xy-plane with identical tiles such that no two tiles overlap and no gap is left between the tiles. Suppose that we can choose tiles of the following shapes: equilateral triangle, square, regular pentagon, regular hexagon. Then the tiling can be done with tiles of

Question 6 :
For construction of a $\triangle PQR$, where $\displaystyle QR=6\ cm, PR=10\ cm$ and $\angle Q=90^{\circ}$, its steps for construction is given below in jumbled form. Identify the third step from the following.<br/><br/>1. At point $ Q $, draw an angle of $ {90}^{\circ} $.<br/>2. From $ R $ cut an arc of length $ PR = 10.0 \ cm $ using a compass.&#160;<br/>3. Name the point of intersection of the arm of the angle $ {90}^{\circ} $ and the arc drawn in step 3, as $ P $.<br/>4. Join $P $ to $ Q $&#160;. $ PQR $ is the required triangle.&#160;<br/>5. Draw the base side $ QR = 6\ &#160;cm $.

Question 7 :
The steps for construction of $\triangle DEF$ with $DE = 4\ cm, EF=6.5\ cm$ and $DF = 8.6\ cm$ are given below in jumbled order:<br/>1. Draw arcs of length $4\ cm$ from $4\ cm$ from $D$ and $6.5\ cm$ from $F$ and mark the intersection point as $E$.<br/>2. Join $D-E$ and $F-E$.<br/>3. Draw a line segment of length $DF = 8.6\ cm$.<br/><br/>The correct order of the steps is:

Question 9 :
The number of triangles with any three of the length 1, 4, 6 and 8 cms, as sides is<br>

Question 11 :
If $b=3, c=4, \angle B=\dfrac{\pi}{3}$, then the number of triangles that can be constructed is

Question 12 :
For construction of a $\triangle PQR$, where $\displaystyle QR=6\ cm, PR=10\ cm$ and $\angle Q=90^{\circ}$, its steps for construction is given below in jumbled form. Identify the fourth step from the following.<br/><br/>1. At point $ Q $, draw an angle of $ {90}^{\circ} $.<br/>2. From $ R $ cut an arc of length $ PR = 10.0 \ cm $ using a compass .<br/>3. Name the point of intersection of the arm of the angle $ {90}^{\circ} $ and the arc drawn in step 3, as $ P $.<br/>4. Join $P $ to $ Q $&#160;. $ PQR $ is the required triangle.&#160;<br/>5. Draw the base side $ QR = 6\ &#160;cm $.

Question 13 :
The sides $A B , B C , C A$ of a triangle $A B C$ have $3,4$ and $5$ interior points respectively on them. Thenumber of triangles that can be constructed using these points as vertices is

Question 14 :
Construct an isosceles$\triangle XYZ,$ where $YZ=5$ units and $\angle XYZ=35^{o}$. Also, find the measure of $\angle YXZ$.

Question 15 :
Construct a triangle $ABC$ in which $AB = 5 cm$ and $BC = 4.6 cm$ and $AC =3.7 cm$<br>Steps for the construction is given in jumbled form.Choose the appropriate sequence for the above<br>1) With radius as $5\ cm$ from $C$, cut an arc.<br>2)They arcs will intersect at point $A$. Join $AB$ and $AC$. $ABC$ is the required triangle.<br>3)Draw a line segment $BC = 4\ cm.$<br>4)With radius as $3$ cm from $B$, cut the arc.

Question 16 :
For construction of a $\triangle PQR$, where $\displaystyle QR=6\ cm, PR=10\ cm$ and $\angle Q=90^{\circ}$, its steps for construction is given below in jumbled form. Identify the second step from the following.<br/><br/>1. At point $ Q $, draw an angle of $ {90}^{\circ} $.<br/>2. From $ R $ cut an arc of length $ PR = 10.0 \ cm $ using a compass.<br/>3. Name the point of intersection of the arm of the angle $ {90}^{\circ} $ and the arc drawn in step 3, as $ P $.<br/>4. Join $P $ to $ Q $&#160;. $ PQR $ is the required triangle.&#160;<br/>5. Draw the base side $ QR = 6\ &#160;cm $.

Question 17 :
Construct a right angled $\triangle ABC$ with $\angle B = 90^\circ, BC = 5\ cm$ and $AC = 10\ cm$ and find the the length of side $AB$

Question 18 :
For construction of a $\triangle PQR$, where&#160;$\displaystyle QR=6\ cm, PR=10\ cm$ and $\angle Q=90^{\circ}$, its steps for construction is given below in jumbled form. Identify the first step from the following.<br/><br/>1. At point $ Q $, draw an angle of $ {90}^{\circ} $.<br/>2. From $ R $ cut an arc of length $ PR = 10.0 \ cm $ using a compass .<br/>3. Name the point of intersection of the arm of the angle $ {90}^{\circ} $ and the arc drawn in step 3, as $ P $.<br/>4. Join $P $ to $ Q $ . $ PQR $ is the required triangle.&#160;<br/>5. Draw the base side $ QR = 6\ &#160;cm $.<br/>

Question 19 :
Mark the correct alternative of the following.<br>In which of the following cases, a right triangle cannot be constructed?

Question 20 :
State the following statement is True or False<br>In a right angle triangle $ABC$ such as $AC=5 cm ,BC=2 cm$ , $\angle B=90^o$<br>Then the length of $AB$ after construction is $7$cm

Question 21 :
Construct a triangle $ABC$, in which $AB = 5.5 cm, AC = 6.5 cm$ and $\angle BAC = 70^{\circ}$.<br/>Steps for its construction is given in a jumbled form.Identify its correct sequence.<br/>1) At $A$, construct a line segment $AE$, sufficiently large, such that $\angle BAC$ at $70^\circ$, use protractor to measure $70^\circ$<br/>2)&#160;Draw a line segment which is sufficiently long using ruler.<br/>3) With $A$ as centre and radius $6.5cm$, draw the line cutting $AE$ at C, join $BC$, then $ABC$ is the required triangle.<br/>4)&#160;Locate points $A$ and $B$ on it such that $AB = 5.5cm$.

Question 22 :
In a right-angled triangle, the square of the hypotenuse is equal to twice the product of the other two sides. One of the acute angles of the triangle is <br/>

Question 23 :
For construction of a $\triangle PQR$, when&#160;$\displaystyle QR=6\ cm, PR=10\ cm$ and $\angle Q=90^{\circ}$, its steps for construction is given below in jumbled form. Identify the fifth step from the following.<br/><br/>1. At point $ Q $, draw an angle of $ {90}^{\circ} $.<br/>2. From $ R $ cut an arc of length $ PR = 10.0 \ cm $ using a compass.<br/>3. Name the point of intersection of the arm of the angle $ {90}^{\circ} $ and the arc drawn in step 3, as $ P $.<br/>4. Join $P $ to $ Q $&#160;. $ PQR $ is the required triangle.&#160;<br/>5. Draw the base side $ QR = 6\ &#160;cm $.

Question 24 :
Length oftwo sides of a $\triangle ABC$is$AB=6\ cm$ and $BC=7\ cm$. Then, which of the following can represent the third side of the triangle ? Also, construct the triangle formed by these three sides.

Question 25 :
The perimeter of a triangle is $45\ cm$. Length of the second side is twice the lengthoffirst side. The third side is $5$ more than the first side. Find the length of each sides and construct the triangle made by these three sides.

Question 26 :
The lengths of the sides of some triangles are given, which of them is not a right angled triangle?<br>

Question 27 :
The sides $AB, BC, CA$ of a trinagle $ABC$ have $3, 4$ and $5$ interior point on them. The number of triangles that can be constructed using these points as vertices are

Question 28 :
Construct an isosceles$\triangle ABC,$ where base $AB=7\ cm$ and $\angle ABC=50^{o}$. Also, find the measure of $\angle ACB$.