RD Sharma Solutions (Ex 3.2): Understanding Quadrilaterals | Mathematics (Maths) Class 8 PDF Download

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RD Sharma Solutions for Class 8 Maths Chapter 16 – 
Understanding Shapes – II (Quadrilaterals) 
EXERCISE 16.1                                                    
 
1. Define the following terms:  
(i) Quadrilateral  
(ii) Convex Quadrilateral 
Solution: 
(i) Quadrilateral 
Definition: Let A, B, C and D be four points in a plane such that: (a) no three of them are 
collinear. (b) The line segments AB, BC, CD and DA do not intersect except at their end 
points. Then an Enclosed figure with four sides is termed as Quadrilateral.  
 
(ii) Convex Quadrilateral 
Definition: If the line containing any side of the quadrilateral has the remaining vertices 
on the same side of it is termed as Convex Quadrilateral. 
 
Vertices A, B lie on the same side of line CD, vertices B, C lie on the same side of line 
DA, vertices C, D lie on the same side of line AB, vertices D, A lie on the same side of 
line BC. 
 
 
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RD Sharma Solutions for Class 8 Maths Chapter 16 – 
Understanding Shapes – II (Quadrilaterals) 
EXERCISE 16.1                                                    
 
1. Define the following terms:  
(i) Quadrilateral  
(ii) Convex Quadrilateral 
Solution: 
(i) Quadrilateral 
Definition: Let A, B, C and D be four points in a plane such that: (a) no three of them are 
collinear. (b) The line segments AB, BC, CD and DA do not intersect except at their end 
points. Then an Enclosed figure with four sides is termed as Quadrilateral.  
 
(ii) Convex Quadrilateral 
Definition: If the line containing any side of the quadrilateral has the remaining vertices 
on the same side of it is termed as Convex Quadrilateral. 
 
Vertices A, B lie on the same side of line CD, vertices B, C lie on the same side of line 
DA, vertices C, D lie on the same side of line AB, vertices D, A lie on the same side of 
line BC. 
 
 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 16 – 
Understanding Shapes – II (Quadrilaterals) 
2. In a quadrilateral, define each of the following: 
(i) Sides 
(ii) Vertices 
(iii) Angles 
(iv) Diagonals 
(v) Adjacent angles 
(vi) Adjacent sides 
(vii) Opposite sides 
(viii) Opposite angles 
(ix) Interior 
(x) Exterior 
Solution: 
 
(i) Sides: In a quadrilateral. All the sides may have same of different length. 
The four line segments AB, BC, CD and DA are called its sides. 
 
(ii) Vertices 
Vertices are the angular points where two sides or edges meet. 
A, B, C and D are the four vertices in a quadrilateral. 
 
(iii) Angles 
Angle is the inclination between two sides of a quadrilateral. i.e. meeting point of two 
sides is an angle. ABC, BCA, CDA and DAB are the four angles in a quadrilateral.  
 
(iv) Diagonals 
The lines joining two opposite vertices is called the diagonals in a quadrilateral. 
BD and AC are the two diagonals. 
 
(v) Adjacent angles 
Angles having one common arm onto the sides is called the adjacent angles. 
ABC, BCD are adjacent angles in a quadrilateral. 
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RD Sharma Solutions for Class 8 Maths Chapter 16 – 
Understanding Shapes – II (Quadrilaterals) 
EXERCISE 16.1                                                    
 
1. Define the following terms:  
(i) Quadrilateral  
(ii) Convex Quadrilateral 
Solution: 
(i) Quadrilateral 
Definition: Let A, B, C and D be four points in a plane such that: (a) no three of them are 
collinear. (b) The line segments AB, BC, CD and DA do not intersect except at their end 
points. Then an Enclosed figure with four sides is termed as Quadrilateral.  
 
(ii) Convex Quadrilateral 
Definition: If the line containing any side of the quadrilateral has the remaining vertices 
on the same side of it is termed as Convex Quadrilateral. 
 
Vertices A, B lie on the same side of line CD, vertices B, C lie on the same side of line 
DA, vertices C, D lie on the same side of line AB, vertices D, A lie on the same side of 
line BC. 
 
 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 16 – 
Understanding Shapes – II (Quadrilaterals) 
2. In a quadrilateral, define each of the following: 
(i) Sides 
(ii) Vertices 
(iii) Angles 
(iv) Diagonals 
(v) Adjacent angles 
(vi) Adjacent sides 
(vii) Opposite sides 
(viii) Opposite angles 
(ix) Interior 
(x) Exterior 
Solution: 
 
(i) Sides: In a quadrilateral. All the sides may have same of different length. 
The four line segments AB, BC, CD and DA are called its sides. 
 
(ii) Vertices 
Vertices are the angular points where two sides or edges meet. 
A, B, C and D are the four vertices in a quadrilateral. 
 
(iii) Angles 
Angle is the inclination between two sides of a quadrilateral. i.e. meeting point of two 
sides is an angle. ABC, BCA, CDA and DAB are the four angles in a quadrilateral.  
 
(iv) Diagonals 
The lines joining two opposite vertices is called the diagonals in a quadrilateral. 
BD and AC are the two diagonals. 
 
(v) Adjacent angles 
Angles having one common arm onto the sides is called the adjacent angles. 
ABC, BCD are adjacent angles in a quadrilateral. 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 16 – 
Understanding Shapes – II (Quadrilaterals) 
(vi) Adjacent sides 
When two sides have common endpoint is termed as adjacent sides. 
AB BC, BC CA, CD DA, DA AB are pairs of adjacent sides in a quadrilateral. 
 
(vii) Opposite sides: Opposite sides when they don’t meet at any point is termed as 
opposite sides.  
AB CD, BC DA are the pairs of opposite sides in a quadrilateral. 
 
(viii) Opposite angles 
Two angles, which are not adjacent angles are termed as opposite angles. 
A and C, angles B and D are opposite angles in a quadrilateral. 
 
(ix) Interior 
The part of plane when points are enclosed within the quadrilateral is called as interior. 
 
(x) Exterior 
The part of plane when points are not enclosed within the quadrilateral is called as 
exterior. 
 
 
3. Complete each of the following, so as to make a true statement: 
(i) A quadrilateral has ________ sides. 
(ii) A quadrilateral has ________angles. 
(iii) A quadrilateral has ________, no three of which are ________. 
(iv) A quadrilateral has ________diagonals. 
(v) The number of pairs of adjacent angles of a quadrilateral is ________. 
(vi) The number of pairs of opposite angles of a quadrilateral is ________. 
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RD Sharma Solutions for Class 8 Maths Chapter 16 – 
Understanding Shapes – II (Quadrilaterals) 
EXERCISE 16.1                                                    
 
1. Define the following terms:  
(i) Quadrilateral  
(ii) Convex Quadrilateral 
Solution: 
(i) Quadrilateral 
Definition: Let A, B, C and D be four points in a plane such that: (a) no three of them are 
collinear. (b) The line segments AB, BC, CD and DA do not intersect except at their end 
points. Then an Enclosed figure with four sides is termed as Quadrilateral.  
 
(ii) Convex Quadrilateral 
Definition: If the line containing any side of the quadrilateral has the remaining vertices 
on the same side of it is termed as Convex Quadrilateral. 
 
Vertices A, B lie on the same side of line CD, vertices B, C lie on the same side of line 
DA, vertices C, D lie on the same side of line AB, vertices D, A lie on the same side of 
line BC. 
 
 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 16 – 
Understanding Shapes – II (Quadrilaterals) 
2. In a quadrilateral, define each of the following: 
(i) Sides 
(ii) Vertices 
(iii) Angles 
(iv) Diagonals 
(v) Adjacent angles 
(vi) Adjacent sides 
(vii) Opposite sides 
(viii) Opposite angles 
(ix) Interior 
(x) Exterior 
Solution: 
 
(i) Sides: In a quadrilateral. All the sides may have same of different length. 
The four line segments AB, BC, CD and DA are called its sides. 
 
(ii) Vertices 
Vertices are the angular points where two sides or edges meet. 
A, B, C and D are the four vertices in a quadrilateral. 
 
(iii) Angles 
Angle is the inclination between two sides of a quadrilateral. i.e. meeting point of two 
sides is an angle. ABC, BCA, CDA and DAB are the four angles in a quadrilateral.  
 
(iv) Diagonals 
The lines joining two opposite vertices is called the diagonals in a quadrilateral. 
BD and AC are the two diagonals. 
 
(v) Adjacent angles 
Angles having one common arm onto the sides is called the adjacent angles. 
ABC, BCD are adjacent angles in a quadrilateral. 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 16 – 
Understanding Shapes – II (Quadrilaterals) 
(vi) Adjacent sides 
When two sides have common endpoint is termed as adjacent sides. 
AB BC, BC CA, CD DA, DA AB are pairs of adjacent sides in a quadrilateral. 
 
(vii) Opposite sides: Opposite sides when they don’t meet at any point is termed as 
opposite sides.  
AB CD, BC DA are the pairs of opposite sides in a quadrilateral. 
 
(viii) Opposite angles 
Two angles, which are not adjacent angles are termed as opposite angles. 
A and C, angles B and D are opposite angles in a quadrilateral. 
 
(ix) Interior 
The part of plane when points are enclosed within the quadrilateral is called as interior. 
 
(x) Exterior 
The part of plane when points are not enclosed within the quadrilateral is called as 
exterior. 
 
 
3. Complete each of the following, so as to make a true statement: 
(i) A quadrilateral has ________ sides. 
(ii) A quadrilateral has ________angles. 
(iii) A quadrilateral has ________, no three of which are ________. 
(iv) A quadrilateral has ________diagonals. 
(v) The number of pairs of adjacent angles of a quadrilateral is ________. 
(vi) The number of pairs of opposite angles of a quadrilateral is ________. 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 16 – 
Understanding Shapes – II (Quadrilaterals) 
(vii) The sum of the angles of a quadrilateral is ________. 
(viii) A diagonal of a quadrilateral is a line segment that joins two ________ vertices 
of the quadrilateral. 
(ix) The sum of the angles of a quadrilateral is ________ right angles. 
(x) The measure of each angle of a convex quadrilateral is ________ 180°. 
(xi) In a quadrilateral the point of intersection of the diagonals lies in ________ of 
the quadrilateral. 
(xii) A point is in the interior of a convex quadrilateral, if it is in the ________ of its 
two opposite angles. 
(xiii) A quadrilateral is convex if for each side, the remaining ________ lie on the 
same side of the line containing the side. 
Solution: 
(i) A quadrilateral has four sides. 
(ii) A quadrilateral has four angles. 
(iii) A quadrilateral has four, no three of which are collinear. 
(iv) A quadrilateral has two diagonals. 
(v) The number of pairs of adjacent angles of a quadrilateral is four. 
(vi) The number of pairs of opposite angles of a quadrilateral is two. 
(vii) The sum of the angles of a quadrilateral is 360
0
. 
(viii) A diagonal of a quadrilateral is a line segment that joins two opposite vertices of 
the quadrilateral. 
(ix) The sum of the angles of a quadrilateral is four right angles. 
(x) The measure of each angle of a convex quadrilateral is less than 180°. 
(xi) In a quadrilateral the point of intersection of the diagonals lies in interior of the 
quadrilateral. 
(xii) A point is in the interior of a convex quadrilateral, if it is in the interiors of its two 
opposite angles. 
(xiii) A quadrilateral is convex if for each side, the remaining vertices lie on the same 
side of the line containing the side. 
 
4. In Fig. 16.19, ABCD is a quadrilateral. 
 
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RD Sharma Solutions for Class 8 Maths Chapter 16 – 
Understanding Shapes – II (Quadrilaterals) 
EXERCISE 16.1                                                    
 
1. Define the following terms:  
(i) Quadrilateral  
(ii) Convex Quadrilateral 
Solution: 
(i) Quadrilateral 
Definition: Let A, B, C and D be four points in a plane such that: (a) no three of them are 
collinear. (b) The line segments AB, BC, CD and DA do not intersect except at their end 
points. Then an Enclosed figure with four sides is termed as Quadrilateral.  
 
(ii) Convex Quadrilateral 
Definition: If the line containing any side of the quadrilateral has the remaining vertices 
on the same side of it is termed as Convex Quadrilateral. 
 
Vertices A, B lie on the same side of line CD, vertices B, C lie on the same side of line 
DA, vertices C, D lie on the same side of line AB, vertices D, A lie on the same side of 
line BC. 
 
 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 16 – 
Understanding Shapes – II (Quadrilaterals) 
2. In a quadrilateral, define each of the following: 
(i) Sides 
(ii) Vertices 
(iii) Angles 
(iv) Diagonals 
(v) Adjacent angles 
(vi) Adjacent sides 
(vii) Opposite sides 
(viii) Opposite angles 
(ix) Interior 
(x) Exterior 
Solution: 
 
(i) Sides: In a quadrilateral. All the sides may have same of different length. 
The four line segments AB, BC, CD and DA are called its sides. 
 
(ii) Vertices 
Vertices are the angular points where two sides or edges meet. 
A, B, C and D are the four vertices in a quadrilateral. 
 
(iii) Angles 
Angle is the inclination between two sides of a quadrilateral. i.e. meeting point of two 
sides is an angle. ABC, BCA, CDA and DAB are the four angles in a quadrilateral.  
 
(iv) Diagonals 
The lines joining two opposite vertices is called the diagonals in a quadrilateral. 
BD and AC are the two diagonals. 
 
(v) Adjacent angles 
Angles having one common arm onto the sides is called the adjacent angles. 
ABC, BCD are adjacent angles in a quadrilateral. 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 16 – 
Understanding Shapes – II (Quadrilaterals) 
(vi) Adjacent sides 
When two sides have common endpoint is termed as adjacent sides. 
AB BC, BC CA, CD DA, DA AB are pairs of adjacent sides in a quadrilateral. 
 
(vii) Opposite sides: Opposite sides when they don’t meet at any point is termed as 
opposite sides.  
AB CD, BC DA are the pairs of opposite sides in a quadrilateral. 
 
(viii) Opposite angles 
Two angles, which are not adjacent angles are termed as opposite angles. 
A and C, angles B and D are opposite angles in a quadrilateral. 
 
(ix) Interior 
The part of plane when points are enclosed within the quadrilateral is called as interior. 
 
(x) Exterior 
The part of plane when points are not enclosed within the quadrilateral is called as 
exterior. 
 
 
3. Complete each of the following, so as to make a true statement: 
(i) A quadrilateral has ________ sides. 
(ii) A quadrilateral has ________angles. 
(iii) A quadrilateral has ________, no three of which are ________. 
(iv) A quadrilateral has ________diagonals. 
(v) The number of pairs of adjacent angles of a quadrilateral is ________. 
(vi) The number of pairs of opposite angles of a quadrilateral is ________. 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 16 – 
Understanding Shapes – II (Quadrilaterals) 
(vii) The sum of the angles of a quadrilateral is ________. 
(viii) A diagonal of a quadrilateral is a line segment that joins two ________ vertices 
of the quadrilateral. 
(ix) The sum of the angles of a quadrilateral is ________ right angles. 
(x) The measure of each angle of a convex quadrilateral is ________ 180°. 
(xi) In a quadrilateral the point of intersection of the diagonals lies in ________ of 
the quadrilateral. 
(xii) A point is in the interior of a convex quadrilateral, if it is in the ________ of its 
two opposite angles. 
(xiii) A quadrilateral is convex if for each side, the remaining ________ lie on the 
same side of the line containing the side. 
Solution: 
(i) A quadrilateral has four sides. 
(ii) A quadrilateral has four angles. 
(iii) A quadrilateral has four, no three of which are collinear. 
(iv) A quadrilateral has two diagonals. 
(v) The number of pairs of adjacent angles of a quadrilateral is four. 
(vi) The number of pairs of opposite angles of a quadrilateral is two. 
(vii) The sum of the angles of a quadrilateral is 360
0
. 
(viii) A diagonal of a quadrilateral is a line segment that joins two opposite vertices of 
the quadrilateral. 
(ix) The sum of the angles of a quadrilateral is four right angles. 
(x) The measure of each angle of a convex quadrilateral is less than 180°. 
(xi) In a quadrilateral the point of intersection of the diagonals lies in interior of the 
quadrilateral. 
(xii) A point is in the interior of a convex quadrilateral, if it is in the interiors of its two 
opposite angles. 
(xiii) A quadrilateral is convex if for each side, the remaining vertices lie on the same 
side of the line containing the side. 
 
4. In Fig. 16.19, ABCD is a quadrilateral. 
 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 16 – 
Understanding Shapes – II (Quadrilaterals) 
(i) Name a pair of adjacent sides. 
(ii) Name a pair of opposite sides. 
(iii) How many pairs of adjacent sides are there? 
(iv) How many pairs of opposite sides are there? 
(v) Name a pair of adjacent angles. 
(vi) Name a pair of opposite angles. 
(vii) How many pairs of adjacent angles are there? 
(viii) How many pairs of opposite angles are there? 
Solution: 
(i) Name a pair of adjacent sides. 
Adjacent sides are: AB, BC or BC, CD or CD, DA or AD, AB 
 
(ii) Name a pair of opposite sides. 
opposite sides are: AB, CD or BC, DA 
 
(iii) How many pairs of adjacent sides are there? 
Four pairs of adjacent sides i.e. AB BC, BC CD, CD DA and DA AB 
 
(iv) How many pairs of opposite sides are there? 
Two pairs of opposite sides. AB, DC and DA, BC 
 
(v) Name a pair of adjacent angles. 
Four pairs of Adjacent angles are: D ?AB A ?BC, A ?BC B ?CA, B ?CA C ?DA or 
C ?DA D ?AB 
 
(vi) Name a pair of opposite angles. 
Four pair of opposite angles are: D ?AB B ?CA and A ?BC C ?DA 
 
(vii) How many pairs of adjacent angles are there? 
Four pairs of adjacent angles. D ?AB A ?BC, A ?BC B ?CA, B ?CA C ?DA and C ?DA 
D ?AB 
 
(viii) How many pairs of opposite angles are there? 
Two pairs of opposite angles. D ?AB B ?CA and A ?BC C ?DA 
 
5. The angles of a quadrilateral are 110°, 72°, 55° and x°. Find the value of x. 
Solution: 
We know that Sum of angles of a quadrilateral is = 360°