RD Sharma MCQs: Congruent Triangles

 Page 1


   
  
    
      
   
       
       
 
Question:57
Mark the correct alternative in each of the following:
If ABC ?
?LKM, then side of ?LKM equal to side AC of ?ABC is
a
LK
b
KM
c
LM
d
None of these
Solution:
It is given that 
As triangles are congruent, same sides will be equal.
So 
Hence 
c .
Question:58
If ?ABC ?
?ABC is isosceles with
a
Page 2


   
  
    
      
   
       
       
 
Question:57
Mark the correct alternative in each of the following:
If ABC ?
?LKM, then side of ?LKM equal to side AC of ?ABC is
a
LK
b
KM
c
LM
d
None of these
Solution:
It is given that 
As triangles are congruent, same sides will be equal.
So 
Hence 
c .
Question:58
If ?ABC ?
?ABC is isosceles with
a
AB = AC
b
AB = BC
c
AC = BC
d
None of these
Solution:
It is given that and  is isosceles
Since triangles are congruent so  as same side are equal
Hence 
a .
Question:59
If ?ABC ?
 ?PQR and ?ABC is not congruent to ?RPQ, then which of the following is not true:
a
BC = PQ
b
AC = PR
c
AB = PQ
d
QR = BC
Solution:
If  and is not congruent to 
Since  and compare corresponding sides you will see
(As )
Hence
a , is not true.
Question:60
In triangles ABC and PQR three equality relations between some parts are as follows:
AB = QP, ?B = ?P and BC = PR
State which of the congruence conditions applies:
a
SAS
b
ASA
c
SSS
d
RHS
 
Solution:
Page 3


   
  
    
      
   
       
       
 
Question:57
Mark the correct alternative in each of the following:
If ABC ?
?LKM, then side of ?LKM equal to side AC of ?ABC is
a
LK
b
KM
c
LM
d
None of these
Solution:
It is given that 
As triangles are congruent, same sides will be equal.
So 
Hence 
c .
Question:58
If ?ABC ?
?ABC is isosceles with
a
AB = AC
b
AB = BC
c
AC = BC
d
None of these
Solution:
It is given that and  is isosceles
Since triangles are congruent so  as same side are equal
Hence 
a .
Question:59
If ?ABC ?
 ?PQR and ?ABC is not congruent to ?RPQ, then which of the following is not true:
a
BC = PQ
b
AC = PR
c
AB = PQ
d
QR = BC
Solution:
If  and is not congruent to 
Since  and compare corresponding sides you will see
(As )
Hence
a , is not true.
Question:60
In triangles ABC and PQR three equality relations between some parts are as follows:
AB = QP, ?B = ?P and BC = PR
State which of the congruence conditions applies:
a
SAS
b
ASA
c
SSS
d
RHS
 
Solution:
In  and
It is given that
Since two sides and an angle are equal so it obeys
Hence
a .
Question:61
In triangles ABC and PQR, if ?A = ?R, ?B = ?P and AB = RP, then which one of the following congruence conditions applies:
a
SAS
b
ASA
c
SSS
d
RHS
Solution:
In  and
It is given that
Since given two sides and an angle are equal so it obeys
Hence
b .
Question:62
In ?PQR ?
?EFD then ED =
a
PQ
b
QR
c
PR
d
None of these
Solution:
If 
We have to find
Since , as in congruent triangles equal sides are decided on the basis of “how they are named”. 
Hence
Page 4


   
  
    
      
   
       
       
 
Question:57
Mark the correct alternative in each of the following:
If ABC ?
?LKM, then side of ?LKM equal to side AC of ?ABC is
a
LK
b
KM
c
LM
d
None of these
Solution:
It is given that 
As triangles are congruent, same sides will be equal.
So 
Hence 
c .
Question:58
If ?ABC ?
?ABC is isosceles with
a
AB = AC
b
AB = BC
c
AC = BC
d
None of these
Solution:
It is given that and  is isosceles
Since triangles are congruent so  as same side are equal
Hence 
a .
Question:59
If ?ABC ?
 ?PQR and ?ABC is not congruent to ?RPQ, then which of the following is not true:
a
BC = PQ
b
AC = PR
c
AB = PQ
d
QR = BC
Solution:
If  and is not congruent to 
Since  and compare corresponding sides you will see
(As )
Hence
a , is not true.
Question:60
In triangles ABC and PQR three equality relations between some parts are as follows:
AB = QP, ?B = ?P and BC = PR
State which of the congruence conditions applies:
a
SAS
b
ASA
c
SSS
d
RHS
 
Solution:
In  and
It is given that
Since two sides and an angle are equal so it obeys
Hence
a .
Question:61
In triangles ABC and PQR, if ?A = ?R, ?B = ?P and AB = RP, then which one of the following congruence conditions applies:
a
SAS
b
ASA
c
SSS
d
RHS
Solution:
In  and
It is given that
Since given two sides and an angle are equal so it obeys
Hence
b .
Question:62
In ?PQR ?
?EFD then ED =
a
PQ
b
QR
c
PR
d
None of these
Solution:
If 
We have to find
Since , as in congruent triangles equal sides are decided on the basis of “how they are named”. 
Hence
c .
Question:63
If ?PQR ?
?EFD, then ?E =
a
?P
b
?Q
c
?R
d
None of these
Solution:
If 
Then we have to find
From the given congruence , as equal angles or equal sides are decided by the location of the letters in naming the
triangles. 
Hence
a
Question:64
In a ?ABC, if AB = AC and BC is produced to D such that ?ACD = 100°, then ?A =
a
20°
b
40°
c
60°
d
80°
Solution:
In the triangle ABC it is given that 
We have to find
Now 
linearpair
Page 5


   
  
    
      
   
       
       
 
Question:57
Mark the correct alternative in each of the following:
If ABC ?
?LKM, then side of ?LKM equal to side AC of ?ABC is
a
LK
b
KM
c
LM
d
None of these
Solution:
It is given that 
As triangles are congruent, same sides will be equal.
So 
Hence 
c .
Question:58
If ?ABC ?
?ABC is isosceles with
a
AB = AC
b
AB = BC
c
AC = BC
d
None of these
Solution:
It is given that and  is isosceles
Since triangles are congruent so  as same side are equal
Hence 
a .
Question:59
If ?ABC ?
 ?PQR and ?ABC is not congruent to ?RPQ, then which of the following is not true:
a
BC = PQ
b
AC = PR
c
AB = PQ
d
QR = BC
Solution:
If  and is not congruent to 
Since  and compare corresponding sides you will see
(As )
Hence
a , is not true.
Question:60
In triangles ABC and PQR three equality relations between some parts are as follows:
AB = QP, ?B = ?P and BC = PR
State which of the congruence conditions applies:
a
SAS
b
ASA
c
SSS
d
RHS
 
Solution:
In  and
It is given that
Since two sides and an angle are equal so it obeys
Hence
a .
Question:61
In triangles ABC and PQR, if ?A = ?R, ?B = ?P and AB = RP, then which one of the following congruence conditions applies:
a
SAS
b
ASA
c
SSS
d
RHS
Solution:
In  and
It is given that
Since given two sides and an angle are equal so it obeys
Hence
b .
Question:62
In ?PQR ?
?EFD then ED =
a
PQ
b
QR
c
PR
d
None of these
Solution:
If 
We have to find
Since , as in congruent triangles equal sides are decided on the basis of “how they are named”. 
Hence
c .
Question:63
If ?PQR ?
?EFD, then ?E =
a
?P
b
?Q
c
?R
d
None of these
Solution:
If 
Then we have to find
From the given congruence , as equal angles or equal sides are decided by the location of the letters in naming the
triangles. 
Hence
a
Question:64
In a ?ABC, if AB = AC and BC is produced to D such that ?ACD = 100°, then ?A =
a
20°
b
40°
c
60°
d
80°
Solution:
In the triangle ABC it is given that 
We have to find
Now 
linearpair
Since
So,
byisoscelestriangle
This implies that
Now, 
Propertyoftriangle
Hence 
a .
Question:65
In an isosceles triangle, if the vertex angle is twice the sum of the base angles, then the measure of vertex angle of the triangle
is
a
100°
b
120°
c
110°
d
130°
Solution:
Let be isosceles triangle 
Then
Now it is given that vertex angle is 2 times the sum of base angles 
(As )
Now 
Propertyoftriangle
(Since , and )