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Page 1
77
In the figure alongside, some points
and some line segments joining them
have been drawn.
Which of these figures is a triangle?
Which figure is not a triangle? Why
not?
?ABC has three sides. Line segment AB is one side. Write the names of the other two
sides. ?ABC has three angles. ?ABC is one of them. Write the names of the other angles.
Points A, B and C are called the vertices of the triangle.
A triangle is a closed figure made by joining three non-collinear points by line segments.
The vertices, sides and angles of a triangle are called the parts of the triangle.
Types of Triangles - Based on Sides
Measure the sides of the following triangles in centimetres, using a divider and ruler.
Enter the lengths in the table below. What do you observe?
‘Length of line segment AB’ is written as l(AB).
In ? ABC In ? PQR In ? XYZ
l(AB) = ..... cm
l(BC) = ..... cm
l(AC) = ..... cm
l(QR) = ..... cm
l(PQ) = ..... cm
l(PR) = ..... cm
l(XY) = .... cm
l(YZ) = .... cm
l(XZ) = .... cm
C
A
B
P
Q
R S
A
B
C
P
Q R
X
Y
Z
15 Triangles and their Properties
Let’s discuss.
Let’s learn.
Page 2
77
In the figure alongside, some points
and some line segments joining them
have been drawn.
Which of these figures is a triangle?
Which figure is not a triangle? Why
not?
?ABC has three sides. Line segment AB is one side. Write the names of the other two
sides. ?ABC has three angles. ?ABC is one of them. Write the names of the other angles.
Points A, B and C are called the vertices of the triangle.
A triangle is a closed figure made by joining three non-collinear points by line segments.
The vertices, sides and angles of a triangle are called the parts of the triangle.
Types of Triangles - Based on Sides
Measure the sides of the following triangles in centimetres, using a divider and ruler.
Enter the lengths in the table below. What do you observe?
‘Length of line segment AB’ is written as l(AB).
In ? ABC In ? PQR In ? XYZ
l(AB) = ..... cm
l(BC) = ..... cm
l(AC) = ..... cm
l(QR) = ..... cm
l(PQ) = ..... cm
l(PR) = ..... cm
l(XY) = .... cm
l(YZ) = .... cm
l(XZ) = .... cm
C
A
B
P
Q
R S
A
B
C
P
Q R
X
Y
Z
15 Triangles and their Properties
Let’s discuss.
Let’s learn.
78
In the table above, the lengths of all sides of ?ABC are equal. Therefore, this triangle
is an equilateral triangle. ‘Lateral’ refers to the sides of a figure.
A triangle with all three sides equal is called an equilateral triangle.
In ?PQR, the length of the two sides PQ and PR are equal. ?PQR is called an
isosceles triangle.
A triangle with two equal sides is called an isosceles triangle.
The lengths of the sides of ?XYZ are all different. Such a triangle is called a scalene
triangle.
A triangle with no two sides equal is called a scalene triangle.
Types of Triangles - Based on Angles
Measure all the angles of the triangles given below. Enter them in the following table. In ? DEF In ? PQR In ? LMN
Measure of ?D = m?D =.....°
Measure of ?E = m?E = .....°
Measure of ?F = ..... = .....°
Measure of ?P = m?P =.....°
Measure of ?Q = ..... = .....°
Measure of ?R = ..... = .....°
Measure of ?L = .....°
Measure of ?M = .....°
Measure of ?N = .....°
Observations: All three angles
are acute angles.
One angle is a right angle and
two are acute angles.
One angle is an obtuse
angle and two are acute.
In the figures above, ?DEF is an acute angled triangle.
A triangle with all three acute angles is called an acute angled triangle.
?PQR is a right angled triangle.
A triangle with one right angle is a right angled triangle.
?LMN is an obtuse angled triangle.
A triangle with one obtuse angle is called an obtuse angled triangle.
Observe the set squares in your compass box.
What kind of triangles are they?
Try this.
D
E
F
P
Q R
L
M N
Page 3
77
In the figure alongside, some points
and some line segments joining them
have been drawn.
Which of these figures is a triangle?
Which figure is not a triangle? Why
not?
?ABC has three sides. Line segment AB is one side. Write the names of the other two
sides. ?ABC has three angles. ?ABC is one of them. Write the names of the other angles.
Points A, B and C are called the vertices of the triangle.
A triangle is a closed figure made by joining three non-collinear points by line segments.
The vertices, sides and angles of a triangle are called the parts of the triangle.
Types of Triangles - Based on Sides
Measure the sides of the following triangles in centimetres, using a divider and ruler.
Enter the lengths in the table below. What do you observe?
‘Length of line segment AB’ is written as l(AB).
In ? ABC In ? PQR In ? XYZ
l(AB) = ..... cm
l(BC) = ..... cm
l(AC) = ..... cm
l(QR) = ..... cm
l(PQ) = ..... cm
l(PR) = ..... cm
l(XY) = .... cm
l(YZ) = .... cm
l(XZ) = .... cm
C
A
B
P
Q
R S
A
B
C
P
Q R
X
Y
Z
15 Triangles and their Properties
Let’s discuss.
Let’s learn.
78
In the table above, the lengths of all sides of ?ABC are equal. Therefore, this triangle
is an equilateral triangle. ‘Lateral’ refers to the sides of a figure.
A triangle with all three sides equal is called an equilateral triangle.
In ?PQR, the length of the two sides PQ and PR are equal. ?PQR is called an
isosceles triangle.
A triangle with two equal sides is called an isosceles triangle.
The lengths of the sides of ?XYZ are all different. Such a triangle is called a scalene
triangle.
A triangle with no two sides equal is called a scalene triangle.
Types of Triangles - Based on Angles
Measure all the angles of the triangles given below. Enter them in the following table. In ? DEF In ? PQR In ? LMN
Measure of ?D = m?D =.....°
Measure of ?E = m?E = .....°
Measure of ?F = ..... = .....°
Measure of ?P = m?P =.....°
Measure of ?Q = ..... = .....°
Measure of ?R = ..... = .....°
Measure of ?L = .....°
Measure of ?M = .....°
Measure of ?N = .....°
Observations: All three angles
are acute angles.
One angle is a right angle and
two are acute angles.
One angle is an obtuse
angle and two are acute.
In the figures above, ?DEF is an acute angled triangle.
A triangle with all three acute angles is called an acute angled triangle.
?PQR is a right angled triangle.
A triangle with one right angle is a right angled triangle.
?LMN is an obtuse angled triangle.
A triangle with one obtuse angle is called an obtuse angled triangle.
Observe the set squares in your compass box.
What kind of triangles are they?
Try this.
D
E
F
P
Q R
L
M N
79
Properties of a Triangle
Activity : Take a triangular piece of paper. Choose three different colours or signs to
mark the three corners of the triangle on both sides of the paper. Fold the
paper at the midpoints of two sides as shown in the pictures.
m?A + m?B + m?C = 180°
Activity : Take a triangular piece of paper and make three different types of marks
near the three angles. Take a point approximately at the centre of the
triangle. From this point, draw three lines that meet the three sides. Cut
the paper along those lines. Place the three angles side by side as shown.
See how the three angles of a triangle together form a straight angle, or, an angle that
measures 180°.
The sum of the measures of the three angles of a triangle is 180°.
Activity : Draw any triangle on a paper. Name its vertices A, B, C. Measure the lengths
of its three sides using a divider and scale and enter them in the table.
Length of side Sum of the length of two sides Length of the third side
l(AB) = .... cm
l(BC) = .... cm
l(AC) = .... cm
l(AB) + l(BC) = .... cm
l(BC) + l(AC) = .... cm
l(AC) + l(AB) = .... cm
l(AC) = ....... cm
l(AB) = ....... cm
l(BC) = ....... cm
The sum of the lengths of any two sides of a triangle
is always greater than the length of the third side.
II
I
III
I
II
III
Try this.
A
B
C
Now I know -
Now I know -
Page 4
77
In the figure alongside, some points
and some line segments joining them
have been drawn.
Which of these figures is a triangle?
Which figure is not a triangle? Why
not?
?ABC has three sides. Line segment AB is one side. Write the names of the other two
sides. ?ABC has three angles. ?ABC is one of them. Write the names of the other angles.
Points A, B and C are called the vertices of the triangle.
A triangle is a closed figure made by joining three non-collinear points by line segments.
The vertices, sides and angles of a triangle are called the parts of the triangle.
Types of Triangles - Based on Sides
Measure the sides of the following triangles in centimetres, using a divider and ruler.
Enter the lengths in the table below. What do you observe?
‘Length of line segment AB’ is written as l(AB).
In ? ABC In ? PQR In ? XYZ
l(AB) = ..... cm
l(BC) = ..... cm
l(AC) = ..... cm
l(QR) = ..... cm
l(PQ) = ..... cm
l(PR) = ..... cm
l(XY) = .... cm
l(YZ) = .... cm
l(XZ) = .... cm
C
A
B
P
Q
R S
A
B
C
P
Q R
X
Y
Z
15 Triangles and their Properties
Let’s discuss.
Let’s learn.
78
In the table above, the lengths of all sides of ?ABC are equal. Therefore, this triangle
is an equilateral triangle. ‘Lateral’ refers to the sides of a figure.
A triangle with all three sides equal is called an equilateral triangle.
In ?PQR, the length of the two sides PQ and PR are equal. ?PQR is called an
isosceles triangle.
A triangle with two equal sides is called an isosceles triangle.
The lengths of the sides of ?XYZ are all different. Such a triangle is called a scalene
triangle.
A triangle with no two sides equal is called a scalene triangle.
Types of Triangles - Based on Angles
Measure all the angles of the triangles given below. Enter them in the following table. In ? DEF In ? PQR In ? LMN
Measure of ?D = m?D =.....°
Measure of ?E = m?E = .....°
Measure of ?F = ..... = .....°
Measure of ?P = m?P =.....°
Measure of ?Q = ..... = .....°
Measure of ?R = ..... = .....°
Measure of ?L = .....°
Measure of ?M = .....°
Measure of ?N = .....°
Observations: All three angles
are acute angles.
One angle is a right angle and
two are acute angles.
One angle is an obtuse
angle and two are acute.
In the figures above, ?DEF is an acute angled triangle.
A triangle with all three acute angles is called an acute angled triangle.
?PQR is a right angled triangle.
A triangle with one right angle is a right angled triangle.
?LMN is an obtuse angled triangle.
A triangle with one obtuse angle is called an obtuse angled triangle.
Observe the set squares in your compass box.
What kind of triangles are they?
Try this.
D
E
F
P
Q R
L
M N
79
Properties of a Triangle
Activity : Take a triangular piece of paper. Choose three different colours or signs to
mark the three corners of the triangle on both sides of the paper. Fold the
paper at the midpoints of two sides as shown in the pictures.
m?A + m?B + m?C = 180°
Activity : Take a triangular piece of paper and make three different types of marks
near the three angles. Take a point approximately at the centre of the
triangle. From this point, draw three lines that meet the three sides. Cut
the paper along those lines. Place the three angles side by side as shown.
See how the three angles of a triangle together form a straight angle, or, an angle that
measures 180°.
The sum of the measures of the three angles of a triangle is 180°.
Activity : Draw any triangle on a paper. Name its vertices A, B, C. Measure the lengths
of its three sides using a divider and scale and enter them in the table.
Length of side Sum of the length of two sides Length of the third side
l(AB) = .... cm
l(BC) = .... cm
l(AC) = .... cm
l(AB) + l(BC) = .... cm
l(BC) + l(AC) = .... cm
l(AC) + l(AB) = .... cm
l(AC) = ....... cm
l(AB) = ....... cm
l(BC) = ....... cm
The sum of the lengths of any two sides of a triangle
is always greater than the length of the third side.
II
I
III
I
II
III
Try this.
A
B
C
Now I know -
Now I know -
80
1. Observe the figures below and write the type of the triangle based on its angles.
?PQR is ...... triangle. ?XYZ is ...... triangle. ?LMN is ...... triangle.
2. Observe the figures below and write the type of the triangle based on its sides.
?ABC is ..... triangle. ?DEF is ...... triangle. ?UVW is ...... triangle.
3. As shown in the figure, Avinash is standing
near his house. He can choose from two
roads to go to school. Which way is
shorter? Explain why.
4. The lengths of the sides of some triangles are given. Say what types of triangles they
are.
(1) 3 cm, 4 cm, 5 cm (2) 3.4 cm, 3.4 cm, 5 cm
(3) 4.3 cm, 4.3 cm, 4.3 cm (4) 3.7 cm, 3.4 cm, 4 cm
5. The lengths of three segments are given for constructing a triangle. Say whether a
triangle with these sides can be drawn. Give the reason for your answer.
(1) 17 cm, 7 cm, 8 cm (2) 7 cm, 24 cm, 25 cm
(3) 9 cm, 6 cm, 16 cm (4) 8.4 cm, 16.4 cm, 4.9 cm
(5) 15 cm, 20 cm, 25 cm (6) 12 cm, 12 cm, 16 cm
?????? Q
P
R
125°
X
Y Z
70°
48°
62°
L
M N
A
C
B
D
E F
U
V W
Practice Set 36
A B
C
Read More
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30 videos|112 docs|15 tests
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FAQs on Textbook: Triangles and their Properties - Mathematics Class 6 (Maharashtra Board)
| 1. What are the different types of triangles based on their sides? |  |
Ans. There are three types of triangles based on their sides: equilateral, isosceles, and scalene. An equilateral triangle has all three sides equal in length. An isosceles triangle has two sides that are equal, while the third side is different. A scalene triangle has all sides of different lengths.
| 2. How do you classify triangles based on their angles? | |
Ans. Triangles can also be classified based on their angles into three categories: acute, right, and obtuse. An acute triangle has all angles less than 90 degrees, a right triangle has one angle exactly equal to 90 degrees, and an obtuse triangle has one angle greater than 90 degrees.
| 3. What is the sum of the interior angles of a triangle? | |
Ans. The sum of the interior angles of any triangle is always 180 degrees. This property holds true for all types of triangles, regardless of their shape or size.
| 4. What are the properties of an equilateral triangle? | |
Ans. An equilateral triangle has several unique properties: all three sides are equal in length, all three interior angles are equal and measure 60 degrees, and it has three lines of symmetry. Additionally, the altitude, median, and angle bisector from each vertex coincide.
| 5. How do you calculate the area of a triangle? | |
Ans. The area of a triangle can be calculated using the formula: Area = 1/2 × base × height. The base is any one side of the triangle, and the height is the perpendicular distance from the base to the opposite vertex. This formula applies to all types of triangles.
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Oct 02, 2025
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