Construction of Triangles

Q.

Two sides of triangle are of lengths 5 cm and 1.5 cm. The length of the third side of the triangle cannot be

1. 3.6 cm

2. 3.4 cm

3. 4.1 cm

4. 3.8 cm

Q.

What are the $3$conditions for formation of triangle by $3$vectors?

Q.

If a, b and c are the lengths of the three sides of a triangle, then which of the following is true?

1. a – b < c

2. a + b < c

3. None of the above

4. a + b = c

Q. How to construct a triangle when all three sides are given?

Q.

Draw an equilateral triangle with sides equal to 6 cm. Construct the incircle and circumcircle for the triangle. Which of the following is true?

1. Incentre and circumcentre are different points

2. Radius of the circumcircle is four times the radius of the incircle

3. Incentre and circumcentre are same points

4. Radius of the circumcircle is equal to the radius of the incircle

Q.

To construct a triangle we should have at least three points.

1. True
2. False

Q.

Draw a triangle of perimeter 13 centimetres and lengths of sides in the ratio 2 : 3 : 4.

Q. The construction of a triangle LMN in which LM=8 cm, angle L=45⁰​​​​​​​​​​^​​​ is possible when (MN+LN) is?

Q.

Construct a right-angled triangle whose hypotenuse measures 5 cm and the length of one whose sides containing the right angle measures 4.5cm.

Q. To construct a triangle uniquely, the minimum number of elements required is

1. 
   One
2. 
   Two
3. 
   Three
4. 
   Six

Q.

If the bisector of the vertical angle of a triangle bisects the base, prove that the triangle is isosceles.

Q.

Which of the following CANNOT be the length of BC required to construct the triangle ABC such that AC = 7.4 cm and AB = 5 cm?

1. 2.1 cm

2. 4.7 cm

3. All of the above can be the length of BC.

4. 3.5 cm

Q.

Constuct an equilateral triangle , each of whose altitudes measures 5.4 cm. Measure each of its sides.

Q. In the given figure, ∆PQR is an isosceles triangle in which PQ=QR, determine the value of x.

Q. If two sides of a triangle is 14cm and 9cm, what is the possible measure of the third side? Options are: 9cm or 2cm or 5cm?

Q.

It is not possible to construct a triangle when its sides are:

1. 3 cm, 5 cm, 5 cm

2. 8.3 cm, 3.4 cm, 6.1 cm

3. 6 cm, 7 cm, 10 cm

4. 5.4 cm, 2.2 cm, 3.1 cm

Q.

While constructing a triangle, which of the following set of lengths can be the sides of a triangle?

1. 2 cm, 4 cm, 1.9 cm

2. 5.5 cm, 6.5 cm, 8.9 cm

3. 1.6 cm, 3.7 cm. 5.3 cm

4. All of the above

Q. The construction of a $\Delta ABC$ in which AB = 7 cm, $\angle A={75}^{\circ }$ is not possible when the difference of BC and AC is equal to

1. 7.6 cm
2. 6.5 cm
3. 6 cm
4. 5.5 cm

Q.

$\text{In each of the following cases, given reasons to show that the construction of}\Delta ABCisnotpossible:\left(i\right)AB=6cm,\angle A={40}^{\circ }and(BC+AC)=5.58cm\left(ii\right)AB=7cm,\angle A={50}^{\circ }and(BC-AC)=8cm\left(iii\right)BC=5cm,\angle B={80}^{\circ },\angle C={50}^{\circ },and\angle A={60}^{\circ }\left(iv\right)AB=4cm,BC=3cm,andAC=7cm.$

Q.

$\Delta$ ABC can be constructed in which AB = 5cm, $\angle$A = 45${}^{\circ }$ and BC + AC = 5cm. State with true or false.

1. False

2. True

Q.

Which of the following given lengths can be the sides of a triangle?

1. 3 cm, 4 cm, 5 cm

2. 1 cm, 2 cm, 3 cm

3. 2 cm, 4 cm, 6 cm

4. 4 cm, 2 cm, 1 cm

Q.

In the construction of $\Delta$ABC, given that BC = 12 cm, is possible when the difference of AB and AC equals

1. True

2. False

3. 10 cm
4. 14 cm

Q.

Construct a $△PQR$ in which $QR=6.2cm,\angle Q=45°,\angle P=35°$. What type of triangle is this?

Q.

For the construction of a triangle by the method of Triangle Construction 3, how many pieces of information/data need to be provided?

1. 1
2. 3
3. 4
4. 2

Q. Which of the following triangles can not be constructed?

1. 
   
   ΔABC in which ∠A = 100°, ∠B = 50° and AB = 5 cm
2. 
   
   ΔABC in which AB = 2 cm, BC = 5 cm and CA = 5 cm
3. 
   
   ΔABC in which ∠A = 30°, ∠B = 60° having perimeter 12 cm
4. 
   
   ΔABC in which AB – AC = 3 cm and ∠B = 45°

Q.

The construction of a triangle ABC, given that BC = 6 cm, B = 45^o is not possible when difference of AB and AC is equal to :

1. 5.2 cm

2. 4.0 cm

3. 5.0 cm

4. 6.9 cm

Q.

Construct $△MAP$ such that $MP=5cm,AP=5cmand\angle P=90°$. Measure other angles of the of the triangle. What type of triangle is this?

Q. 10, 18, and x are the measure of sides of a triangle. Find the range of values of x.

Q. arcs are required to draw the perpendicular bisector in triangle construction 1.

1. 1
2. 2
3. 3
4. 4

Q. In the given construction $\angle MYX={60}^{\circ }$, then $\angle AYX$ is equal to_________(Assuming that PQ and RS are perpendicular bisectors of AX and AY respectively)

1. 
2. 
3. 
4.