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Page 1
81
Quadrilaterals
Take four points A, B, C, D, on a paper, such that any three
of them will be non- collinear. These points are to be joined to make
a closed figure, but in such a way that when any two points are
joined the other two must lie on the same side of that line.
The figure obtained by following the given rule is called a
quadrilateral.
Observe the figures below and say which of them are quadrilaterals.
(i) (ii) (iii) (iv)
Here, figure (i) is that of a quadrilateral.
Like a triangle, quadrilateral ABCD is a closed figure. The four line segments that form
a quadrilateral are called its sides. Seg AB, seg BC, seg CD and seg AD are the four sides
of this quadrilateral. Points A, B, C and D are the vertices of the quadrilateral.
Reading and Writing of a Quadrilateral
? A quadrilateral can be named by starting at any vertex and going serially either
clockwise or anti-clockwise around the figure.
When writing the name of a quadrilateral a sign like this ‘ ’ is put in place of the word
‘quadrilateral’.
Reading Writing
Quadrilateral ADCB ADCB
Quadrilateral DCBA DCBA
Quadrilateral CBAD CBAD
Quadrilateral BADC BADC
Write the names of this quadrilateral starting at any vertex and going anti-clockwise
around the figure.
D
A
B
C
A
B
C
D
D
C
B
A
A
B
C
D
16 Quadrilaterals
Let’s learn.
Page 2
81
Quadrilaterals
Take four points A, B, C, D, on a paper, such that any three
of them will be non- collinear. These points are to be joined to make
a closed figure, but in such a way that when any two points are
joined the other two must lie on the same side of that line.
The figure obtained by following the given rule is called a
quadrilateral.
Observe the figures below and say which of them are quadrilaterals.
(i) (ii) (iii) (iv)
Here, figure (i) is that of a quadrilateral.
Like a triangle, quadrilateral ABCD is a closed figure. The four line segments that form
a quadrilateral are called its sides. Seg AB, seg BC, seg CD and seg AD are the four sides
of this quadrilateral. Points A, B, C and D are the vertices of the quadrilateral.
Reading and Writing of a Quadrilateral
? A quadrilateral can be named by starting at any vertex and going serially either
clockwise or anti-clockwise around the figure.
When writing the name of a quadrilateral a sign like this ‘ ’ is put in place of the word
‘quadrilateral’.
Reading Writing
Quadrilateral ADCB ADCB
Quadrilateral DCBA DCBA
Quadrilateral CBAD CBAD
Quadrilateral BADC BADC
Write the names of this quadrilateral starting at any vertex and going anti-clockwise
around the figure.
D
A
B
C
A
B
C
D
D
C
B
A
A
B
C
D
16 Quadrilaterals
Let’s learn.
82
Adjacent Sides of a Quadrilateral
The sides AB and AD of ABCD have a common vertex A.
Sides AB and AD are adjacent sides.
Name the pairs of adjacent sides in the figure alongside.
(1) ........ and ........ (2) ........ and ........
(3) ........ and ........ (4) ........ and ........
Every quadrilateral has four pairs of adjacent sides.
Adjacent sides of the quadrilateral have a common vertex.
Opposite Sides of a Quadrilateral
In ABCD the sides AB and DC have no common vertex.
Side AB and side DC are opposite sides of the quadrilateral.
Name the pairs of opposite sides of this quadrilateral.
Pairs of opposite sides :
(1) ........ and ........ (2) ........ and ........
Opposite sides of the quadrilateral do not have a common vertex.
Adjacent Angles of a Quadrilateral
Take four straws/ sticks/ strips all of different lengths. Join them to each other to make
a quadrilateral.
Draw its figure. We get the quadrilateral DEFG. The two angles ?DEF and ? GFE
have a common arm EF. These angles are neighbouring or adjacent angles.
Name the adjacent angles of the quadrilateral DEFG.
(1) ........ and ......... (2) ........ and .........
(3) ........ and ......... (4) ........ and .........
The angles of a quadrilateral which have one common arm are called
adjacent angles of the quadrilateral.
G
D
E
F
A
B
C
D
A
B
C
D
Let’s learn.
Page 3
81
Quadrilaterals
Take four points A, B, C, D, on a paper, such that any three
of them will be non- collinear. These points are to be joined to make
a closed figure, but in such a way that when any two points are
joined the other two must lie on the same side of that line.
The figure obtained by following the given rule is called a
quadrilateral.
Observe the figures below and say which of them are quadrilaterals.
(i) (ii) (iii) (iv)
Here, figure (i) is that of a quadrilateral.
Like a triangle, quadrilateral ABCD is a closed figure. The four line segments that form
a quadrilateral are called its sides. Seg AB, seg BC, seg CD and seg AD are the four sides
of this quadrilateral. Points A, B, C and D are the vertices of the quadrilateral.
Reading and Writing of a Quadrilateral
? A quadrilateral can be named by starting at any vertex and going serially either
clockwise or anti-clockwise around the figure.
When writing the name of a quadrilateral a sign like this ‘ ’ is put in place of the word
‘quadrilateral’.
Reading Writing
Quadrilateral ADCB ADCB
Quadrilateral DCBA DCBA
Quadrilateral CBAD CBAD
Quadrilateral BADC BADC
Write the names of this quadrilateral starting at any vertex and going anti-clockwise
around the figure.
D
A
B
C
A
B
C
D
D
C
B
A
A
B
C
D
16 Quadrilaterals
Let’s learn.
82
Adjacent Sides of a Quadrilateral
The sides AB and AD of ABCD have a common vertex A.
Sides AB and AD are adjacent sides.
Name the pairs of adjacent sides in the figure alongside.
(1) ........ and ........ (2) ........ and ........
(3) ........ and ........ (4) ........ and ........
Every quadrilateral has four pairs of adjacent sides.
Adjacent sides of the quadrilateral have a common vertex.
Opposite Sides of a Quadrilateral
In ABCD the sides AB and DC have no common vertex.
Side AB and side DC are opposite sides of the quadrilateral.
Name the pairs of opposite sides of this quadrilateral.
Pairs of opposite sides :
(1) ........ and ........ (2) ........ and ........
Opposite sides of the quadrilateral do not have a common vertex.
Adjacent Angles of a Quadrilateral
Take four straws/ sticks/ strips all of different lengths. Join them to each other to make
a quadrilateral.
Draw its figure. We get the quadrilateral DEFG. The two angles ?DEF and ? GFE
have a common arm EF. These angles are neighbouring or adjacent angles.
Name the adjacent angles of the quadrilateral DEFG.
(1) ........ and ......... (2) ........ and .........
(3) ........ and ......... (4) ........ and .........
The angles of a quadrilateral which have one common arm are called
adjacent angles of the quadrilateral.
G
D
E
F
A
B
C
D
A
B
C
D
Let’s learn.
83
Opposite Angles of a Quadrilateral
In DEFG, the angles ?DEF and ?DGF do not have any common arm. ?DEF and
?DGF lie opposite to each other. Hence they are the opposite angles of a quadrilateral.
Name the other opposite angles in the figure.
1. Angle opposite to ?EFG is ............... 2. Angle opposite to ?FGD is ..............
The angles of a quadrilateral which do not have a common arm are called
opposite angles of a quadrilateral.
Diagonals of a Quadrilateral
In ABCD, the line segments that join the vertices of the
opposite angles ?A and ?C, as also of ?B and ?D, have been
drawn. The segments AC and BD are the diagonals of the
quadrilateral ABCD. The diagonal AC joins the vertices of the
opposite angles ?A and ?C.
The line segments which join the vertices of the opposite angles of a
quadrilateral are the diagonals of the quadrilateral.
In the figure above, name the angles whose vertices are joined by the diagonal BD.
? Cut out a paper in the shape of a quadrilateral. Make folds in it that join the vertices
of opposite angles. What can these folds be called?
? Take two triangular pieces of paper such that one side of one triangle is equal to
one side of the other. Let us suppose that in ?ABC and ?PQR, sides AC and PQ
are the equal sides.
A D
B C
C
P
R
Q
A
B
Try this.
Page 4
81
Quadrilaterals
Take four points A, B, C, D, on a paper, such that any three
of them will be non- collinear. These points are to be joined to make
a closed figure, but in such a way that when any two points are
joined the other two must lie on the same side of that line.
The figure obtained by following the given rule is called a
quadrilateral.
Observe the figures below and say which of them are quadrilaterals.
(i) (ii) (iii) (iv)
Here, figure (i) is that of a quadrilateral.
Like a triangle, quadrilateral ABCD is a closed figure. The four line segments that form
a quadrilateral are called its sides. Seg AB, seg BC, seg CD and seg AD are the four sides
of this quadrilateral. Points A, B, C and D are the vertices of the quadrilateral.
Reading and Writing of a Quadrilateral
? A quadrilateral can be named by starting at any vertex and going serially either
clockwise or anti-clockwise around the figure.
When writing the name of a quadrilateral a sign like this ‘ ’ is put in place of the word
‘quadrilateral’.
Reading Writing
Quadrilateral ADCB ADCB
Quadrilateral DCBA DCBA
Quadrilateral CBAD CBAD
Quadrilateral BADC BADC
Write the names of this quadrilateral starting at any vertex and going anti-clockwise
around the figure.
D
A
B
C
A
B
C
D
D
C
B
A
A
B
C
D
16 Quadrilaterals
Let’s learn.
82
Adjacent Sides of a Quadrilateral
The sides AB and AD of ABCD have a common vertex A.
Sides AB and AD are adjacent sides.
Name the pairs of adjacent sides in the figure alongside.
(1) ........ and ........ (2) ........ and ........
(3) ........ and ........ (4) ........ and ........
Every quadrilateral has four pairs of adjacent sides.
Adjacent sides of the quadrilateral have a common vertex.
Opposite Sides of a Quadrilateral
In ABCD the sides AB and DC have no common vertex.
Side AB and side DC are opposite sides of the quadrilateral.
Name the pairs of opposite sides of this quadrilateral.
Pairs of opposite sides :
(1) ........ and ........ (2) ........ and ........
Opposite sides of the quadrilateral do not have a common vertex.
Adjacent Angles of a Quadrilateral
Take four straws/ sticks/ strips all of different lengths. Join them to each other to make
a quadrilateral.
Draw its figure. We get the quadrilateral DEFG. The two angles ?DEF and ? GFE
have a common arm EF. These angles are neighbouring or adjacent angles.
Name the adjacent angles of the quadrilateral DEFG.
(1) ........ and ......... (2) ........ and .........
(3) ........ and ......... (4) ........ and .........
The angles of a quadrilateral which have one common arm are called
adjacent angles of the quadrilateral.
G
D
E
F
A
B
C
D
A
B
C
D
Let’s learn.
83
Opposite Angles of a Quadrilateral
In DEFG, the angles ?DEF and ?DGF do not have any common arm. ?DEF and
?DGF lie opposite to each other. Hence they are the opposite angles of a quadrilateral.
Name the other opposite angles in the figure.
1. Angle opposite to ?EFG is ............... 2. Angle opposite to ?FGD is ..............
The angles of a quadrilateral which do not have a common arm are called
opposite angles of a quadrilateral.
Diagonals of a Quadrilateral
In ABCD, the line segments that join the vertices of the
opposite angles ?A and ?C, as also of ?B and ?D, have been
drawn. The segments AC and BD are the diagonals of the
quadrilateral ABCD. The diagonal AC joins the vertices of the
opposite angles ?A and ?C.
The line segments which join the vertices of the opposite angles of a
quadrilateral are the diagonals of the quadrilateral.
In the figure above, name the angles whose vertices are joined by the diagonal BD.
? Cut out a paper in the shape of a quadrilateral. Make folds in it that join the vertices
of opposite angles. What can these folds be called?
? Take two triangular pieces of paper such that one side of one triangle is equal to
one side of the other. Let us suppose that in ?ABC and ?PQR, sides AC and PQ
are the equal sides.
A D
B C
C
P
R
Q
A
B
Try this.
84
P
S
R
Q
B
C
E
D
A
Try this.
? Join the triangles so that their equal sides lie side by side.
What figure do we get?
We used two triangles to obtain a quadrilateral. The sum of the three angles of a
triangle is 180°. Hence, what will the sum of the angles of a quadrilateral be?
Draw a quadrilateral. Draw one diagonal of this quadrilateral
and divide it into two triangles. Measure all the angles in the
figure.
Is the sum of the measures of the four angles of the
quadrilateral equal to the sum of the measures of the six
angles of the two triangles?
Verify that this is so with other quadrilaterals.
? The sum of the measures of the four angles of a quadrilateral
= 180° + 180° = 360°
The sum of the measures of the four angles of a quadrilateral is 360°.
Polygons
? You must have seen the five-petal flowers of tagar, kunda or sadaphuli.
Draw a picture of one of those flowers. Join the tips of the petals one by one. What
is the figure you get? The closed figure obtained in this way by joining five points by five
line segments is called a pentagon.
(1) Write the names of the vertices of the pentagon.
(2) Name the sides of the pentagon. (3) Name the angles of the pentagon.
(4) See if you can sometimes find players on a field forming a pentagon.
Triangles, quadrilaterals, pentagons and other closed figures with more than five sides
are all called polygons.
Let’s learn.
Now I know -
Page 5
81
Quadrilaterals
Take four points A, B, C, D, on a paper, such that any three
of them will be non- collinear. These points are to be joined to make
a closed figure, but in such a way that when any two points are
joined the other two must lie on the same side of that line.
The figure obtained by following the given rule is called a
quadrilateral.
Observe the figures below and say which of them are quadrilaterals.
(i) (ii) (iii) (iv)
Here, figure (i) is that of a quadrilateral.
Like a triangle, quadrilateral ABCD is a closed figure. The four line segments that form
a quadrilateral are called its sides. Seg AB, seg BC, seg CD and seg AD are the four sides
of this quadrilateral. Points A, B, C and D are the vertices of the quadrilateral.
Reading and Writing of a Quadrilateral
? A quadrilateral can be named by starting at any vertex and going serially either
clockwise or anti-clockwise around the figure.
When writing the name of a quadrilateral a sign like this ‘ ’ is put in place of the word
‘quadrilateral’.
Reading Writing
Quadrilateral ADCB ADCB
Quadrilateral DCBA DCBA
Quadrilateral CBAD CBAD
Quadrilateral BADC BADC
Write the names of this quadrilateral starting at any vertex and going anti-clockwise
around the figure.
D
A
B
C
A
B
C
D
D
C
B
A
A
B
C
D
16 Quadrilaterals
Let’s learn.
82
Adjacent Sides of a Quadrilateral
The sides AB and AD of ABCD have a common vertex A.
Sides AB and AD are adjacent sides.
Name the pairs of adjacent sides in the figure alongside.
(1) ........ and ........ (2) ........ and ........
(3) ........ and ........ (4) ........ and ........
Every quadrilateral has four pairs of adjacent sides.
Adjacent sides of the quadrilateral have a common vertex.
Opposite Sides of a Quadrilateral
In ABCD the sides AB and DC have no common vertex.
Side AB and side DC are opposite sides of the quadrilateral.
Name the pairs of opposite sides of this quadrilateral.
Pairs of opposite sides :
(1) ........ and ........ (2) ........ and ........
Opposite sides of the quadrilateral do not have a common vertex.
Adjacent Angles of a Quadrilateral
Take four straws/ sticks/ strips all of different lengths. Join them to each other to make
a quadrilateral.
Draw its figure. We get the quadrilateral DEFG. The two angles ?DEF and ? GFE
have a common arm EF. These angles are neighbouring or adjacent angles.
Name the adjacent angles of the quadrilateral DEFG.
(1) ........ and ......... (2) ........ and .........
(3) ........ and ......... (4) ........ and .........
The angles of a quadrilateral which have one common arm are called
adjacent angles of the quadrilateral.
G
D
E
F
A
B
C
D
A
B
C
D
Let’s learn.
83
Opposite Angles of a Quadrilateral
In DEFG, the angles ?DEF and ?DGF do not have any common arm. ?DEF and
?DGF lie opposite to each other. Hence they are the opposite angles of a quadrilateral.
Name the other opposite angles in the figure.
1. Angle opposite to ?EFG is ............... 2. Angle opposite to ?FGD is ..............
The angles of a quadrilateral which do not have a common arm are called
opposite angles of a quadrilateral.
Diagonals of a Quadrilateral
In ABCD, the line segments that join the vertices of the
opposite angles ?A and ?C, as also of ?B and ?D, have been
drawn. The segments AC and BD are the diagonals of the
quadrilateral ABCD. The diagonal AC joins the vertices of the
opposite angles ?A and ?C.
The line segments which join the vertices of the opposite angles of a
quadrilateral are the diagonals of the quadrilateral.
In the figure above, name the angles whose vertices are joined by the diagonal BD.
? Cut out a paper in the shape of a quadrilateral. Make folds in it that join the vertices
of opposite angles. What can these folds be called?
? Take two triangular pieces of paper such that one side of one triangle is equal to
one side of the other. Let us suppose that in ?ABC and ?PQR, sides AC and PQ
are the equal sides.
A D
B C
C
P
R
Q
A
B
Try this.
84
P
S
R
Q
B
C
E
D
A
Try this.
? Join the triangles so that their equal sides lie side by side.
What figure do we get?
We used two triangles to obtain a quadrilateral. The sum of the three angles of a
triangle is 180°. Hence, what will the sum of the angles of a quadrilateral be?
Draw a quadrilateral. Draw one diagonal of this quadrilateral
and divide it into two triangles. Measure all the angles in the
figure.
Is the sum of the measures of the four angles of the
quadrilateral equal to the sum of the measures of the six
angles of the two triangles?
Verify that this is so with other quadrilaterals.
? The sum of the measures of the four angles of a quadrilateral
= 180° + 180° = 360°
The sum of the measures of the four angles of a quadrilateral is 360°.
Polygons
? You must have seen the five-petal flowers of tagar, kunda or sadaphuli.
Draw a picture of one of those flowers. Join the tips of the petals one by one. What
is the figure you get? The closed figure obtained in this way by joining five points by five
line segments is called a pentagon.
(1) Write the names of the vertices of the pentagon.
(2) Name the sides of the pentagon. (3) Name the angles of the pentagon.
(4) See if you can sometimes find players on a field forming a pentagon.
Triangles, quadrilaterals, pentagons and other closed figures with more than five sides
are all called polygons.
Let’s learn.
Now I know -
85
Cut out a pentagonal piece of paper. How many triangles do we get if we fold or cut
along the dotted lines shown in the figure? Now can you find the sum of the angles of
a pentagon?
? Make other triangles by folding in different ways. Note your observations.
? Observe the figures below and find out their names.
Figure Name Figure Name
(1) (3)
(2) (4)
Do this activity in groups of four. From your compass boxes, collect set squares of
the same shapes and place them side by side in all possible different ways. What figures
do you get? Write their names.
(a) Two set squares (b) Three set squares (c) Four set squares
1. Draw XYZW and name the following.
(1) The pairs of opposite angles. (2) The pairs of opposite sides.
(3) The pairs of adjacent sides. (4) The pairs of adjacent angles.
(5) The diagonals of the quadrilateral.
(6) The name of the quadrilateral in different ways.
Practice Set 37
Practice Set 38
Try this.
Try this.
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FAQs on Textbook: Quadrilaterals - Mathematics Class 6 (Maharashtra Board)
| 1. What are the different types of quadrilaterals? |  |
Ans. There are several types of quadrilaterals, including squares, rectangles, rhombuses, parallelograms, trapezoids (or trapeziums), and kites. Each type has its unique properties. For instance, a square has all sides equal and all angles right angles, while a rectangle has opposite sides equal and all angles right angles.
| 2. How can we calculate the area of a quadrilateral? | |
Ans. The area of a quadrilateral can be calculated using different formulas depending on its type. For example, for a rectangle, the area is found by multiplying the length by the width. For a trapezoid, the area can be calculated using the formula: Area = 1/2 × (Base1 + Base2) × Height. For irregular quadrilaterals, it may be necessary to divide the shape into triangles and sum their areas.
| 3. What are the properties of a parallelogram? | |
Ans. A parallelogram has several key properties: opposite sides are equal in length, opposite angles are equal, the diagonals bisect each other, and the sum of adjacent angles is 180 degrees. These properties help distinguish parallelograms from other quadrilaterals.
| 4. How do the angles in a quadrilateral add up? | |
Ans. The sum of the interior angles of any quadrilateral is always 360 degrees. This means that if you know the measures of three angles, you can easily find the fourth angle by subtracting the sum of the known angles from 360 degrees.
| 5. What is the difference between a rectangle and a rhombus? | |
Ans. The primary difference between a rectangle and a rhombus lies in their properties. A rectangle has opposite sides that are equal and all angles are right angles. A rhombus, on the other hand, has all sides equal in length, but angles are not necessarily right angles. In fact, the angles in a rhombus can be acute or obtuse.
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Oct 14, 2025
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