RD Sharma MCQs: Quadrilaterals | Mathematics (Maths) Class 9 PDF Download

 Page 1


                     
   
      
 
 
          
 
       
      
      
 
       
Q u e s t i o n : 6 4
Mark the correct alternative in each of the following:
The opposite sides of a quadrilateral have
a
no common point
b
one common point
c
two common points
d
infinitely many common points
Page 2


                     
   
      
 
 
          
 
       
      
      
 
       
Q u e s t i o n : 6 4
Mark the correct alternative in each of the following:
The opposite sides of a quadrilateral have
a
no common point
b
one common point
c
two common points
d
infinitely many common points
S o l u t i o n :
We can look at a quadrilateral as:
The opposite sides of the above quadrilateral AB and CD have no point in common.
Hence the correct choice is a
.
Q u e s t i o n : 6 5
The consecutive sides of a quadrilateral have
a
no common point
b
one common point
c
two common points
d
infinitely many common points
S o l u t i o n :
We can look at a quadrilateral as:
The consecutive sides of the above quadrilateral AB and BC have one point in common.
Hence the correct choice is b
.
Q u e s t i o n : 6 6
PQRS is a quadrilateral, PR and QS intersect each other at O. In which of the following cases, PQRS is a
parallelogram?
a
?P = 100°, ?Q = 80°, ?R = 95°
b
  ?P =85°, ?Q = 85°, ?R = 95°
c
PQ = 7 cm, QR = 7 cm, RS = 8 cm, SP = 8 cm
d
Page 3


                     
   
      
 
 
          
 
       
      
      
 
       
Q u e s t i o n : 6 4
Mark the correct alternative in each of the following:
The opposite sides of a quadrilateral have
a
no common point
b
one common point
c
two common points
d
infinitely many common points
S o l u t i o n :
We can look at a quadrilateral as:
The opposite sides of the above quadrilateral AB and CD have no point in common.
Hence the correct choice is a
.
Q u e s t i o n : 6 5
The consecutive sides of a quadrilateral have
a
no common point
b
one common point
c
two common points
d
infinitely many common points
S o l u t i o n :
We can look at a quadrilateral as:
The consecutive sides of the above quadrilateral AB and BC have one point in common.
Hence the correct choice is b
.
Q u e s t i o n : 6 6
PQRS is a quadrilateral, PR and QS intersect each other at O. In which of the following cases, PQRS is a
parallelogram?
a
?P = 100°, ?Q = 80°, ?R = 95°
b
  ?P =85°, ?Q = 85°, ?R = 95°
c
PQ = 7 cm, QR = 7 cm, RS = 8 cm, SP = 8 cm
d
OP = 6.5 cm, OQ = 6.5 cm, OR = 5.2 cm, OS = 5.2 cm
S o l u t i o n :
Let us analyze each case one by one.
We have a quadrilateral named PQRS, with diagonals PR and QS intersecting at O.
a
, ,
By angle sum property of a quadrilateral, we get:
Clearly, 
And 
Thus we have PQRS a quadrilateral with opposite angles are equal.
Therefore,
PQRS is a parallelogram.
b
, ,
By angle sum property of a quadrilateral, we get:
Clearly, 
And
Thus we have PQRS a quadrilateral with opposite angles are not equal.
Therefore,
PQRS is not a parallelogram.
c
, , ,
Clearly, 
And
Thus we have PQRS a quadrilateral with opposite sides are not equal
Therefore,
PQRS is not a parallelogram.
c
, , ,
We know that the diagonals of a parallelogram bisect each other.
But, here we have
Page 4


                     
   
      
 
 
          
 
       
      
      
 
       
Q u e s t i o n : 6 4
Mark the correct alternative in each of the following:
The opposite sides of a quadrilateral have
a
no common point
b
one common point
c
two common points
d
infinitely many common points
S o l u t i o n :
We can look at a quadrilateral as:
The opposite sides of the above quadrilateral AB and CD have no point in common.
Hence the correct choice is a
.
Q u e s t i o n : 6 5
The consecutive sides of a quadrilateral have
a
no common point
b
one common point
c
two common points
d
infinitely many common points
S o l u t i o n :
We can look at a quadrilateral as:
The consecutive sides of the above quadrilateral AB and BC have one point in common.
Hence the correct choice is b
.
Q u e s t i o n : 6 6
PQRS is a quadrilateral, PR and QS intersect each other at O. In which of the following cases, PQRS is a
parallelogram?
a
?P = 100°, ?Q = 80°, ?R = 95°
b
  ?P =85°, ?Q = 85°, ?R = 95°
c
PQ = 7 cm, QR = 7 cm, RS = 8 cm, SP = 8 cm
d
OP = 6.5 cm, OQ = 6.5 cm, OR = 5.2 cm, OS = 5.2 cm
S o l u t i o n :
Let us analyze each case one by one.
We have a quadrilateral named PQRS, with diagonals PR and QS intersecting at O.
a
, ,
By angle sum property of a quadrilateral, we get:
Clearly, 
And 
Thus we have PQRS a quadrilateral with opposite angles are equal.
Therefore,
PQRS is a parallelogram.
b
, ,
By angle sum property of a quadrilateral, we get:
Clearly, 
And
Thus we have PQRS a quadrilateral with opposite angles are not equal.
Therefore,
PQRS is not a parallelogram.
c
, , ,
Clearly, 
And
Thus we have PQRS a quadrilateral with opposite sides are not equal
Therefore,
PQRS is not a parallelogram.
c
, , ,
We know that the diagonals of a parallelogram bisect each other.
But, here we have
And
Therefore,
PQRS is not a parallelogram. 
Hence, the correct choice is a
.
Q u e s t i o n : 6 7
Which  of the following quadrilateral is not a rhombus?
a
All four sides are equal
b
Diagonals bisect each other
c
Diagonals bisect opposite angles
d
One angle between the diagonals is 60°
S o l u t i o n :
Let us consider the rhombus ABCD as:
We have the following properties of a rhombus:
All four sides are equal.
Diagonals bisect each other at right angles.
Hence the correct choice is d
.
Q u e s t i o n : 6 8
Diagonals necessarily bisect opposite angles in a
a
rectangle
b
parallelogram
c
isosceles trapezium
d
Page 5


                     
   
      
 
 
          
 
       
      
      
 
       
Q u e s t i o n : 6 4
Mark the correct alternative in each of the following:
The opposite sides of a quadrilateral have
a
no common point
b
one common point
c
two common points
d
infinitely many common points
S o l u t i o n :
We can look at a quadrilateral as:
The opposite sides of the above quadrilateral AB and CD have no point in common.
Hence the correct choice is a
.
Q u e s t i o n : 6 5
The consecutive sides of a quadrilateral have
a
no common point
b
one common point
c
two common points
d
infinitely many common points
S o l u t i o n :
We can look at a quadrilateral as:
The consecutive sides of the above quadrilateral AB and BC have one point in common.
Hence the correct choice is b
.
Q u e s t i o n : 6 6
PQRS is a quadrilateral, PR and QS intersect each other at O. In which of the following cases, PQRS is a
parallelogram?
a
?P = 100°, ?Q = 80°, ?R = 95°
b
  ?P =85°, ?Q = 85°, ?R = 95°
c
PQ = 7 cm, QR = 7 cm, RS = 8 cm, SP = 8 cm
d
OP = 6.5 cm, OQ = 6.5 cm, OR = 5.2 cm, OS = 5.2 cm
S o l u t i o n :
Let us analyze each case one by one.
We have a quadrilateral named PQRS, with diagonals PR and QS intersecting at O.
a
, ,
By angle sum property of a quadrilateral, we get:
Clearly, 
And 
Thus we have PQRS a quadrilateral with opposite angles are equal.
Therefore,
PQRS is a parallelogram.
b
, ,
By angle sum property of a quadrilateral, we get:
Clearly, 
And
Thus we have PQRS a quadrilateral with opposite angles are not equal.
Therefore,
PQRS is not a parallelogram.
c
, , ,
Clearly, 
And
Thus we have PQRS a quadrilateral with opposite sides are not equal
Therefore,
PQRS is not a parallelogram.
c
, , ,
We know that the diagonals of a parallelogram bisect each other.
But, here we have
And
Therefore,
PQRS is not a parallelogram. 
Hence, the correct choice is a
.
Q u e s t i o n : 6 7
Which  of the following quadrilateral is not a rhombus?
a
All four sides are equal
b
Diagonals bisect each other
c
Diagonals bisect opposite angles
d
One angle between the diagonals is 60°
S o l u t i o n :
Let us consider the rhombus ABCD as:
We have the following properties of a rhombus:
All four sides are equal.
Diagonals bisect each other at right angles.
Hence the correct choice is d
.
Q u e s t i o n : 6 8
Diagonals necessarily bisect opposite angles in a
a
rectangle
b
parallelogram
c
isosceles trapezium
d
square
S o l u t i o n :
From the given choices, only in a square the diagonals bisect the opposite angles.
Let us prove it.
Take the following square ABCD with diagonal AD.
In and :
 Oppositesidesofasquareareequal.
 Common
 Oppositesidesofasquareareequal.
Thus,
 BySSSCongruenceRule
By Corresponding parts of congruent triangles property we have:
Therefore, in a square the diagonals bisect the opposite angles.
Hence the correct choice is d
.
Q u e s t i o n : 6 9
The two diagonals are equal in a
a
parallelogram
b
rhombus
c
rectangle
d
trapezium
S o l u t i o n :
Two diagonals are equal only in a rectangle.
This can be proved as follows: