Construction of Similar Triangles

Q. Construct $∆$ ABC such that $\angle$B = ${100}^{°}$ , BC = 6.4 cm, $\angle$C = ${50}^{°}$ and construct its incircle.

Q.

The point of concurrence of the three angle bisectors of a triangle, is called

1. Centroid

2. Circumcentre

3. Orthocentre

4. Incentre

Q. We cannot draw a unique triangle when only are given.

1. three sides
2. three angles
3. a side and two angle

Q. What data must be given to construct an equilateral triangle using a compass and a ruler?

1. One side
2. One angle
3. Two sides
4. One angle and one side

Q. It is possible to construct a triangle with the side lengths of 2, 4, 5.

1. False
2. True

Q.

If you are asked to construct $△$APQ $\sim$ $△$ABC with the scale factor $\frac{3}{5}$, which of the following is incorrect?
Given: In $△ABC,AB=4cm$, $BC=3cm$ and $\angle ABC={90}^{\circ }$.
$A_1{A}_2=A_2{A}_3=A_3{A}_4=A_4{A}_5$.​​​​​​

1. $\angle AQP=\angle ACB$

2. $\angle A{A}_{3}P=\angle A{A}_{5}P$

3. $AP:PB=3:2$

4. 5PQ = 3BC

Q.

Prove that equilateral ∆ can be constructed on any given line segment .

Q.

The point of concurrence of the three angle bisectors of a triangle, is called

1. Circumcentre

2. Orthocentre

3. Centroid

4. Incentre

Q. If a triangle PQR is constructed similar to triangle ABC and is smaller than the triangle ABC, then the scale factor is .

1. less than 1
2. greater than 1
3. equal to 1

Q. If an equilateral triangle is scaled by 3 : 5, then the ratio of its original area to the new area is .

1. 9 : 25
2. 3 : 5
3. 6 : 10

Q. Identify the triangle that is similar to the triangle AOB, given same colored angles are of equal measure.

1. 
2. 
3. 

Q. When a triangle similar to an equilateral triangle of side 6 cm is constructed at a scale of 1 : 3, then the sides of the new triangle is .

1. 1 cm
2. 2 cm
3. 3 cm

Q. Are two isosceles triangles an equilateral triangle?

1. Yes
2. No
3. Can't say

Q. One side of an equilateral triangle is 24 cm. The mid-points of its sides are joined to form another triangle is formed by joining the midpoints of this triangle and the process is continued indefinitely. Determine the sum of the perimeters of all such triangles.

Q.

While constructing a triangle, we need to consider sum of angles in a triangle as?

1. 220 degrees

2. 180 degrees

3. 235 degrees

4. 360 degrees

Q. In $\Delta ABC,AB=BC=6cm$. A circle is drawn with center at B and radius 2 cm. What is the scale factor of the triangle formed by the point B and the points where the circle intersects $△ABC$?

1. $1$
2. $\frac{1}{3}$
3. $\frac{1}{2}$
4. $\frac{2}{3}$

Q. Is it possible to draw a triangle with sides of length 2 cm, 3 cm and 7 cm?

Q. What data must be given to construct an equilateral triangle using a compass and a ruler?

1. One side
2. One angle
3. Two sides
4. One angle and one side

Q.

If you are asked to construct $△$APQ $\sim$ $△$ABC with the scale factor $\frac{3}{5}$, which of the following is incorrect?
Given: In $△ABC,AB=4cm$, $BC=3cm$ and $\angle ABC={90}^{\circ }$.
$A_1{A}_2=A_2{A}_3=A_3{A}_4=A_4{A}_5$.​​​​​​

1. $\angle AQP=\angle ACB$

2. $\angle A{A}_{3}P=\angle A{A}_{5}P$

3. $AP:PB=2:3$

4. 5PQ = 3BC

Q. If the similar triangle constructed is 5/3 times the given one, then 3 parts correspond to the given triangle.

1. True
2. False

Q. The scale factor for constructing similar triangles gives the ratio of corresponding sides of triangles.

1. False
2. True