Construction of Triangle 3

Q.

Triangle ABC has base angles ${30}^{\circ }$ and ${120}^{\circ }$ respectively. The perimeter is $4+2\sqrt{3}$. What type of triangle is this?

1. Right triangle
2. Isosceles triangle
3. Scalene triangle
4. Equilateral triangle

Q. Question 4
Construct the following and give justification :
​​​​​​​
An equilateral triangle, if its altitude is 3.2cm.

Q.

In the given construction of a $\Delta ABC$, $\angle CAB$ will be

1. ${55}^{\circ }$
2. ${45}^{\circ }$
3. ${75}^{\circ }$
4. ${60}^{\circ }$

Q. perpendicular bisectors are required during the construction of a triangle when perimeter of the triangle and two base angles are given.

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

Q. Question 2
In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.

Q. In the figure given below, which of the pairs of triangles are congruent?(Assume that DE and FG are perpendicular bisectors of AX and AY respectively)

1. $△$ ABX and $△$ ACY
2. $△$ ACR and $△$ YCR
3. $△$ ABC and $△$ ACR
4. $△$ ABQ and $△$ XBQ

Q.

In $\Delta PQR$, $\angle PQR={30}^{\circ }\angle PRQ={60}^{\circ }$, QR = 5 cm. Which of the following figures accurately represents the triangle.

1. 

2. 

3. 

4. 

Q. In the given construction of a $\Delta ABC$, $\angle CAB$ will be

1. 
2. 
3. 
4. 

Q.

A $\Delta$ABC can be constructed in which $\angle$B = 60${}^{\circ }$, $\angle$C = 45${}^{\circ }$, and AB + BC + CA = 12cm.

1. True

2. False

Q. Question 5
Write True or False and give reasons for your answer:

A $\Delta ABC$ can be constructed in which $\angle B={105}^{\circ },\angle C={90}^{\circ }$ and AB + BC + CA = 10cm.

Q. Can a $\Delta ABC$ can be constructed in which $\angle B={105}^{\circ },\angle C={90}^{\circ }$ and AB + BC + CA = 10cm.

1. Yes
2. No
3. Cannot be determined
4. Data insufficient

Q. Question 6
Write True or False and give reasons for your answer:

A $\Delta ABC$ can be constructed in which $\angle B={60}^{\circ },\angle C={45}^{\circ }$ and AB + BC + CA = 12cm.

Q.

A triangle ABC has base angle ${45}^{\circ }$. It's perimeter is $[2+\sqrt{2}]$. What type of triangle is it?

1. Isosceles triangle

2. Right triangle

3. Can't be determined

4. Scalene triangle

Q. To construct a triangle ABC in which $\angle B={60}^{\circ },\angle C={45}^{\circ }$ and AB + BC + AC = 12 cm

The steps of construction are:
Step 1: Draw a line segment XY=12 cm
Step 2: At X, construct an angle of ${60}^{\circ }$ and at y construct an angle of ${45}^{\circ }$
Step 3: Bisect these angles. Let bisector of these angles intersect at point A
Step 4 will be

1. Draw perpendicular bisector PQ of XB to intersect XY at B and RS of YC to intersect XY at C
2. Join AB and AC to obtain required $\Delta ABC$
3. Bisect these angles.Let bisector of these angles intersect at point A
4. Draw perpendicular bisector PQ of XA to intersect XY at B and RS of YA to intersect XY at C

Q. $\text{Complete the steps to construct a}\text{triangle XYZ in which}\angle Y={45}^{\circ },\angle Z={90}^{\circ }\text{and XY + YZ + ZX = 13 cm.}$

$\text{Steps of construction:}\text{Step 1: Draw a line segment AB=13 cm.}\text{Step 2: At A, construct an angle of}{45}^{\circ }\text{and at B construct an angle of}{90}^{\circ }.\text{Step 3 will be :}$

1. Bisect these angles. Let bisector of these angles intersect at point X.
2. Draw perpendicular bisector EF of XB to intersect AB at Z
3. Draw perpendicular bisection CD of AX to intersect AB at Y.
4. Join XY and XZ to obtain required triangle XYZ.

Q.

In the given construction,

• PQ is the perpendicular bisector AX
• RS is the perpendicular bisector AY
• XA is the angle bisector of the $\angle LXY$
• YA is the angle bisector of the $\angle MYX$

Then $\angle CAB$ will be

1. ${55}^{\circ }$
2. ${45}^{\circ }$
3. ${75}^{\circ }$
4. ${60}^{\circ }$

Q. Observe the construction given below.
To construct triangle ABC, the given components are

1. Its perimeter and two base angles
2. Its base, a base angle and the sum of other two sides
3. Its base, a base angle and the difference of other two sides
4. Its base, a base angle and perimeter

Q. Question 5
Write True or False and give reasons for your answer:

A $\Delta ABC$ can be constructed in which $\angle B={105}^{\circ },\angle C={90}^{\circ }$ and AB + BC + CA = 10cm.

Q.

Triangle ABC has base angles ${30}^{\circ }$ and ${120}^{\circ }$ respectively. The perimeter is $4+2\sqrt{3}$. What type of triangle is this?

1. Right triangle
2. Isosceles triangle
3. Scalene triangle
4. Equilateral triangle

Q.

A student constructed a triangle when the perimeter of the triangle and both the base angles are given. The steps of construction he used are as follows:

$\text{1. Draw a line segment, say XY equal to}\text{AB + BC + AC.}$

$\text{2. Make}\angle LXY\text{equal to}\angle B\text{and}\angle MYX\text{equal to}\angle C.$

$\text{3. Bisect}\angle LXY\text{and}\angle MYX.\text{Let these}\text{bisectors intersect each other at A.}$

$\text{4. Draw perpendicular bisectors DE of AX}\text{and FG of AY.}$

$\text{5. Let BQ intersect XY at B and RC}\text{intersect XY at C. Join AB and AC.}$

$\text{6. The triangle ABC is thus formed.}$

$\text{How many isosceles triangles are there}\text{in this figure?}$

1. 0
2. 1
3. 2
4. 4