Congruence (Exercise 16.1) RD Sharma Solutions | Mathematics (Maths) Class 7 PDF Download

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1. Explain the concept of congruence of figures with the help of certain examples. 
 
Solution: 
Congruent objects or figures are exact copies of each other or we can say mirror images 
of each other. The relation of two objects being congruent is called congruence. 
Consider Ball 1 and Ball 2. These two balls are congruent. 
 
Ball 1                      Ball 2 
Now consider the two stars below. Star A and Star B are exactly the same in size, colour 
and shape. These are congruent stars 
 
Star A                                        Star B 
 
2. Fill in the blanks: 
(i) Two line segments are congruent if …….. 
(ii) Two angles are congruent if …….. 
(iii) Two square are congruent if ……… 
(iv) Two rectangles are congruent if ……… 
(v) Two circles are congruent if ……. 
 
Solution: 
Page 2


 
 
 
 
  
 
 
 
        
 
1. Explain the concept of congruence of figures with the help of certain examples. 
 
Solution: 
Congruent objects or figures are exact copies of each other or we can say mirror images 
of each other. The relation of two objects being congruent is called congruence. 
Consider Ball 1 and Ball 2. These two balls are congruent. 
 
Ball 1                      Ball 2 
Now consider the two stars below. Star A and Star B are exactly the same in size, colour 
and shape. These are congruent stars 
 
Star A                                        Star B 
 
2. Fill in the blanks: 
(i) Two line segments are congruent if …….. 
(ii) Two angles are congruent if …….. 
(iii) Two square are congruent if ……… 
(iv) Two rectangles are congruent if ……… 
(v) Two circles are congruent if ……. 
 
Solution: 
 
 
 
 
  
 
 
 
(i) They are of equal lengths 
 
(ii) Their measures are the same or equal. 
 
(iii) Their sides are equal or they have the same side length 
 
(iv) Their dimensions are same that is lengths are equal and their breadths are also 
equal.  
 
(v) They have same radii 
 
3. In Fig. 6, ?POQ ??ROS, can we say that ?POR ??QOS 
 
Solution: 
Given that 
?POQ ??ROS  
Also ?ROQ ??ROQ  
Therefore adding ?ROQ to both sides of ?POQ ??ROS,  
We get, ?POQ + ?ROQ ??ROQ + ?ROS  
Therefore, ?POR ??QOS 
 
4. In fig. 7, a = b = c, name the angle which is congruent to ?AOC 
Page 3


 
 
 
 
  
 
 
 
        
 
1. Explain the concept of congruence of figures with the help of certain examples. 
 
Solution: 
Congruent objects or figures are exact copies of each other or we can say mirror images 
of each other. The relation of two objects being congruent is called congruence. 
Consider Ball 1 and Ball 2. These two balls are congruent. 
 
Ball 1                      Ball 2 
Now consider the two stars below. Star A and Star B are exactly the same in size, colour 
and shape. These are congruent stars 
 
Star A                                        Star B 
 
2. Fill in the blanks: 
(i) Two line segments are congruent if …….. 
(ii) Two angles are congruent if …….. 
(iii) Two square are congruent if ……… 
(iv) Two rectangles are congruent if ……… 
(v) Two circles are congruent if ……. 
 
Solution: 
 
 
 
 
  
 
 
 
(i) They are of equal lengths 
 
(ii) Their measures are the same or equal. 
 
(iii) Their sides are equal or they have the same side length 
 
(iv) Their dimensions are same that is lengths are equal and their breadths are also 
equal.  
 
(v) They have same radii 
 
3. In Fig. 6, ?POQ ??ROS, can we say that ?POR ??QOS 
 
Solution: 
Given that 
?POQ ??ROS  
Also ?ROQ ??ROQ  
Therefore adding ?ROQ to both sides of ?POQ ??ROS,  
We get, ?POQ + ?ROQ ??ROQ + ?ROS  
Therefore, ?POR ??QOS 
 
4. In fig. 7, a = b = c, name the angle which is congruent to ?AOC 
 
 
 
 
  
 
 
 
 
Solution: 
From the figure we have 
? AOB = ? BOC = ? COD 
Therefore, ? AOB = ?COD 
Also, ? AOB + ? BOC = ? BOC + ? COD 
? AOC = ? BOD 
Hence, ? BOD ?? AOC 
 
5. Is it correct to say that any two right angles are congruent? Give reasons to justify 
your answer. 
 
Solution: 
Two right angles are congruent to each other because they both measure 90
o
. 
We know that two angles are congruent if they have the same measure. 
 
6. In fig. 8, ?AOC ??PYR and ?BOC ??QYR. Name the angle which is congruent 
to ?AOB. 
 
Solution: 
Given that?AOC ??PYR  
Also given that ?BOC ??QYR  
Page 4


 
 
 
 
  
 
 
 
        
 
1. Explain the concept of congruence of figures with the help of certain examples. 
 
Solution: 
Congruent objects or figures are exact copies of each other or we can say mirror images 
of each other. The relation of two objects being congruent is called congruence. 
Consider Ball 1 and Ball 2. These two balls are congruent. 
 
Ball 1                      Ball 2 
Now consider the two stars below. Star A and Star B are exactly the same in size, colour 
and shape. These are congruent stars 
 
Star A                                        Star B 
 
2. Fill in the blanks: 
(i) Two line segments are congruent if …….. 
(ii) Two angles are congruent if …….. 
(iii) Two square are congruent if ……… 
(iv) Two rectangles are congruent if ……… 
(v) Two circles are congruent if ……. 
 
Solution: 
 
 
 
 
  
 
 
 
(i) They are of equal lengths 
 
(ii) Their measures are the same or equal. 
 
(iii) Their sides are equal or they have the same side length 
 
(iv) Their dimensions are same that is lengths are equal and their breadths are also 
equal.  
 
(v) They have same radii 
 
3. In Fig. 6, ?POQ ??ROS, can we say that ?POR ??QOS 
 
Solution: 
Given that 
?POQ ??ROS  
Also ?ROQ ??ROQ  
Therefore adding ?ROQ to both sides of ?POQ ??ROS,  
We get, ?POQ + ?ROQ ??ROQ + ?ROS  
Therefore, ?POR ??QOS 
 
4. In fig. 7, a = b = c, name the angle which is congruent to ?AOC 
 
 
 
 
  
 
 
 
 
Solution: 
From the figure we have 
? AOB = ? BOC = ? COD 
Therefore, ? AOB = ?COD 
Also, ? AOB + ? BOC = ? BOC + ? COD 
? AOC = ? BOD 
Hence, ? BOD ?? AOC 
 
5. Is it correct to say that any two right angles are congruent? Give reasons to justify 
your answer. 
 
Solution: 
Two right angles are congruent to each other because they both measure 90
o
. 
We know that two angles are congruent if they have the same measure. 
 
6. In fig. 8, ?AOC ??PYR and ?BOC ??QYR. Name the angle which is congruent 
to ?AOB. 
 
Solution: 
Given that?AOC ??PYR  
Also given that ?BOC ??QYR  
 
 
 
 
  
 
 
 
Now, ?AOC = ?AOB + ?BOC and ?PYR =?PYQ +?QYR  
By putting the value of ?AOC and ?PYR in ?AOC ??PYR  
We get, ?AOB + ?BOC ??PYQ + ?QYR  
?AOB ??PYQ (?BOC ??QYR)  
Hence, ?AOB ??PYQ 
 
7. Which of the following statements are true and which are false; 
(i) All squares are congruent. 
(ii) If two squares have equal areas, they are congruent. 
(iii) If two rectangles have equal areas, they are congruent. 
(iv) If two triangles have equal areas, they are congruent. 
 
Solution: 
(i) False. 
Explanation: 
All the sides of a square are of equal length. However, different squares can have sides 
of different lengths. Hence all squares are not congruent. 
 
(ii) True. 
Explanation: 
Two squares that have the same area will have sides of the same lengths. Hence they 
will be congruent. 
 
(iii) False  
Explanation: 
Area of a rectangle = length x breadth 
Two rectangles can have the same area. However, the lengths of their sides can vary 
and hence they are not congruent. 
 
(iv) False 
Explanation: 
Area of a triangle = 1/2 x base x height 
Two triangles can have the same area but the lengths of their sides can vary and hence 
they cannot be congruent.