Introduction to Congruency

Q. If the angles of a triangle are in the ratio 2:3:4, then the difference between the largest and the smallest angle is

1. ${20}^{\circ }$
2. ${30}^{\circ }$
3. ${10}^{\circ }$
4. ${40}^{\circ }$

Q. Which of the following pairs of figures are congruent?

1. 
2. 
3. 
4. 

Q. In $\Delta ABC$, $AB=AC,\angle A={40}^{\circ }$. $O$ is a point inside $\Delta ABC$ such that $\angle OBC=\angle OCA$. Find the measure of $\angle BOC$.

1. ${110}^{\circ }$
2. ${35}^{\circ }$
3. ${140}^{\circ }$
4. ${155}^{\circ }$

Q.

If $\text{A}$ and $\text{B}$ are two events, then the probability of the event that at most one of $\text{A, B}$ occurs, is

1. $\text{P(A’∩B) +P(A∩B’) + P(A’∩B’)}$

2. $\text{1-P(A∩B)}$

3. $\text{P(A’)+P(B’)+P(AUB)-1}$

4. All of the above

Q.

The front and back of a car are asymmetrical.

1. True
2. False

Q.

Solve the equation $x+16=20$ and represents the solution graphically.

Q. What is the solution of the equation $4x+25=7x+10$?

1. $x=4$
2. $x=5$
3. $x=8$
4. $x=10$

Q. Two angles of a triangle are in the ratio $\frac{2}{3}:\frac{3}{2}$ and the third angle is ${50}^{\circ }$. The two angles are:

1. ${45}^{\circ },{85}^{\circ }$
2. ${30}^{\circ },{95}^{\circ }$
3. ${30}^{\circ },{100}^{\circ }$
4. ${40}^{\circ },{90}^{\circ }$

Q. Two triangles are congruent, if they have

1. same shape, equal measure
2. same shape, unequal measure
3. different shape, unequal measure
4. different shape, equal measure

Q. If in two triangles ABC and PQR , AB = PQ, AC = PR and BC = QR, then .

1. ∆ ACB ≅ ∆ PQR
2. ∆ ABC ≅ ∆ PRQ
3. ∆ ABC ≅ ∆ PQR

Q. In the figure below, lines $AB$ and $CD$ intersect at $O$. If $\angle AOC+\angle BOE={70}^{\circ }$ and $\angle BOD={40}^{\circ }$, find $2\angle BOE$.

1. ${50}^{\circ }$
2. ${30}^{\circ }$
3. ${60}^{\circ }$
4. ${90}^{\circ }$

Q. Which of the following parameters should be exactly same for two objects to be congruent?

1. Only size
2. Neither shape nor size
3. Both shape and size
4. Only shape

Q. $\mathrm{The}\mathrm{auxiliary}\mathrm{circle}\mathrm{of}\mathrm{the}\mathrm{hyperbola}\frac{x^2}{9}-\frac{y^2}{16}=1\mathrm{is}{x}^2+y^2=9$

1. False
2. True

Q. Two circles of same radius are not congruent.

1. True
2. False

Q. Two leaves of paper from the same notebook are congruent.

1. False
2. True

Q. Which of the following pairs of figures are congruent?

1. 
2. 
3. 
4. 

Q. The congruent sides of an isoceles triangle are 3 cm each and its perimeter is 10 cm. Find the length of the other side.

1. 4 cm
2. 5 cm
3. 3 cm
4. 6 cm

Q.

Which of the following are congruent?

1. Two squares having the same side

2. Two circles of same radii

3. Two rectangles of same length
4. Two line segments of different lengths

Q. Two line segments are said to be congruent if ______.

1. they have equal length
2. one is twice the length of other
3. the sum of their lengths is 10 cm
4. they have unequal length

Q. Which of the following pair of letters are congruent?

1. A and V
2. p and q
3. E and F
4. c and o