Construction of triangle - class-VI

Question 1 Multiple Choice (Single Answer)

State true or false:

Whether it is possible to construct a triangle or not with its sides equal to $5$ cm, $7$ cm, and $4$ cm
Ans: Yes

True
False

Question 2 Multiple Choice (Single Answer)

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:
1. Draw arcs of length $4\ cm$ from $4\ cm$ from $D$ and $6.5\ cm$ from $F$ and mark the intersection point as $E$.
2. Join $D-E$ and $F-E$.
3. Draw a line segment of length $DF = 8.6\ cm$.

The correct order of the steps is:

$3-1-2$
$1-2-3$
$2-3-1$
$2-1-3$

Question 3 Multiple Choice (Single Answer)

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

Right angled triangle
Isosceles triangle
Equilateral triangle
Scalene triangle

Question 4 Multiple Choice (Single Answer)

The number of triangles with any three of the length 1, 4, 6 and 8 cms, as sides is

4
2
1
0

Question 5 Multiple Choice (Single Answer)

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.

1. At point $ Q $, draw an angle of $ {90}^{\circ} $.
2. From $ R $ cut an arc of length $ PR = 10.0 \ cm $ using a compass.
3. Name the point of intersection of the arm of the angle $ {90}^{\circ} $ and the arc drawn in step 3, as $ P $.
4. Join $P $ to $ Q $ . $ PQR $ is the required triangle.
5. Draw the base side $ QR = 6\ cm $.

$3$
$4$
$2$
$5$
$1$

Question 6 Multiple Choice (Single Answer)

The lengths of the sides of some triangles are given, which of them is not a right angled triangle?

$5$ cm , $12$ cm, $13$ cm
$7$ cm, $24$ cm, $25$ cm
$5$ cm, $8$ cm, 1$0$ cm
$3$ cm, $4$ cm, $5$ cm

Question 7 Multiple Choice (Single Answer)

Construct a right angled triangle $PQR$, in which $\angle Q = 90^\circ $, hypotenuse $PR=8,cm$ and $QR=4.5,cm$. Draw bisector of angle $PQR$ and let it meet $PR$ at point $T$ then $T$ is equidistant from$PQ$ and $QR$.

True
False

Question 8 Multiple Choice (Single Answer)

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

$0$
$1$
$3$
$2$

Question 9 Multiple Choice (Multiple Answers)

Which of the following pair of sides can form triangle?

$5\ cm, 6\ cm , 4\ cm$
$13\ cm , 12\ cm , 24\ cm$
$2\ cm , 7\ cm , 9\ cm$
$5.6\ cm , 6.5\ cm , 12\ cm$

Question 10 Multiple Choice (Single Answer)

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

$205$
$210$
$315$
$216$

Question 11 Multiple Choice (Single Answer)

Mark the correct alternative of the following.
In which of the following cases can a right triangle ABC be constructed?

$AB=5$cm, $BC=7$cm, $AC=10$cm
$AB=7$cm, $BC=8$cm, $AC=12$cm
$AB=8$cm, $BC=17$cm, $AC=15$cm
None of these

Question 12 Multiple Choice (Single Answer)

Mark the correct alternative of the following.
In which of the following cases, a right triangle cannot be constructed?

$12$cm, $5$cm, $13$cm
$8$cm, $6$cm, $10$cm
$5$cm, $9$cm, $11$cm
None of these

Question 13 Multiple Choice (Single Answer)

Construct a $\triangle PQR$ in which $QR= 4.6\ cm., {\angle Q}={\angle R=50 ^{0}}$. Then the perimeter of the triangle is:

$10.2\ cm$
$13.2\ cm$
$11.8\ cm$
$12.4\ cm$

Question 14 Multiple Choice (Single Answer)

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 $AB$

$6.2\ cm$
$5\ cm$
$8.7\ cm$
$7.2\ cm$

Question 15 Multiple Choice (Single Answer)

Construct a $\triangle PQR$ such that $\angle P = 30^\circ, \angle Q = 60^\circ$ and $PQ = 10\ cm$.Find the measure of $\angle R$

$30^\circ$
$45^\circ$
$60^\circ$
$90^\circ$

Question 16 Multiple Choice (Single Answer)

Length of two 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.

$8\ cm$
$13\ cm$
$14\ cm$
$15\ cm$

Question 17 Multiple Choice (Single Answer)

The perimeter of a triangle is $45\ cm$. Length of the second side is twice the length of first 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.

$11,19,15$
$10,20,15$
$10,16,19$
$13,15,17$

Question 18 Multiple Choice (Single Answer)

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

$1,4,3,2$
$4,3,2,1$
$3,1,4,2$
$4,1,3,2$

Question 19 Multiple Choice (Single Answer)

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

$35^{o}$
$70^{o}$
$110^{o}$
$140^{o}$

Question 20 Multiple Choice (Single Answer)

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

$50^{0}$
$80^{o}$
$100^{o}$
$120^{o}$

Question 21 Multiple Choice (Single Answer)

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.

1. At point $ Q $, draw an angle of $ {90}^{\circ} $.
2. From $ R $ cut an arc of length $ PR = 10.0 \ cm $ using a compass .
3. Name the point of intersection of the arm of the angle $ {90}^{\circ} $ and the arc drawn in step 3, as $ P $.
4. Join $P $ to $ Q $ . $ PQR $ is the required triangle.
5. Draw the base side $ QR = 6\ cm $.

$5$
$1$
$2$
$3$
$4$

Question 22 Multiple Choice (Single Answer)

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

True
False

Question 23 Multiple Choice (Single Answer)

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.

1. At point $ Q $, draw an angle of $ {90}^{\circ} $.
2. From $ R $ cut an arc of length $ PR = 10.0 \ cm $ using a compass.
3. Name the point of intersection of the arm of the angle $ {90}^{\circ} $ and the arc drawn in step 3, as $ P $.
4. Join $P $ to $ Q $ . $ PQR $ is the required triangle.
5. Draw the base side $ QR = 6\ cm $.

$2$
$1$
$4$
$5$
$3$

Question 24 Multiple Choice (Single Answer)

For construction of a $\triangle PQR$, when $\displaystyle QR=6\ cm, PR=10\ cm$ and $\angle Q=90^{\circ}$, its steps for construction is given below in jumbled form. Identify the fifth step from the following.

1. At point $ Q $, draw an angle of $ {90}^{\circ} $.
2. From $ R $ cut an arc of length $ PR = 10.0 \ cm $ using a compass.
3. Name the point of intersection of the arm of the angle $ {90}^{\circ} $ and the arc drawn in step 3, as $ P $.
4. Join $P $ to $ Q $ . $ PQR $ is the required triangle.
5. Draw the base side $ QR = 6\ cm $.

$2$
$3$
$1$
$5$
$4$

Question 25 Multiple Choice (Single Answer)

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 first step from the following.

1. At point $ Q $, draw an angle of $ {90}^{\circ} $.
2. From $ R $ cut an arc of length $ PR = 10.0 \ cm $ using a compass .
3. Name the point of intersection of the arm of the angle $ {90}^{\circ} $ and the arc drawn in step 3, as $ P $.
4. Join $P $ to $ Q $ . $ PQR $ is the required triangle.
5. Draw the base side $ QR = 6\ cm $.

$2$
$1$
$3$
$5$
$4$

Question 26 Multiple Choice (Single Answer)

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

$2,4,1,3$
$2,1,4,3$
$1,2,4,3$
$4,2,1,3$

Question 27 Multiple Choice (Single Answer)

Which of the following steps is INCORRECT, while constructing $\triangle$LMN, right angled at M, given that LN = 5 cm and MN = 3 cm?
Step 1. Draw MN of length 3 cm.
Step 2. At M, draw MX $\perp$ MN. (L should be some where on this perpendicular).
Step 3. With N as centre, draw an arc of radius 5 cm. (L must be on this arc, since it is at a distance of 5 cm from N).
Step 4. L has to be on the perpendicular line MX as well as on the arc drawn with centre N. Therefore, L is the meeting point of these two and $\triangle$LMN is obtained.

Only Step 4
Both Step 2 and Step 3
Only Step 2
None of these

Construction of triangle - class-VI

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