Classification of Triangle

In classification of triangle there are six elements in a triangle, that is, three sides and three angles. So, classification of triangle is done on the base of these elements.

Triangles are classified in two ways:

(i) On the basis of sides and,

(ii) On the basis of angles.



According to Sides

Classification of triangles based on their sides. A triangle in which all the sides are equal is called an equilateral triangle. A triangle in which any two sides are equal is called an isosceles triangle. If none of its sides are equal it is called a scalene triangle. Now, let us classify triangles based on their angles.

1. Scalene Triangle:

A triangle in which all the three sides are unequal in length is called a scalene triangle.

Scalene Triangle

AC > BC >AB

6 cm > 5 cm > 4.5 cm.



2. Isosceles Triangle:

A triangle in which two of its sides are equal is called isosceles triangle.

Isosceles Triangle

PQ = PR = 6 cm.



3. Equilateral Triangle:

A triangle in which have all its three sides equal in length is called an equilateral triangle.

Equilateral Triangle

LM = MN = NL = 5.5 cm


According to Angles

1. Acute Triangle:

A triangle which has all the three angles acute that is, less than 90°, is called an acute angled triangle or acute triangle.

In other words, a triangle is which all the three angles are acute is called an acute-angled triangle. 

Acute Triangle

In the given figure ∠A, ∠B and ∠C are acute angle. Thus, ∆ABC is an acute-angled triangle.

2. Obtuse Triangle:

A triangle whose one angle is obtuse or more than 90° but less than 180° is called an obtuse angled triangle or obtuse triangle.


A triangle is which one of its angles is measuring more than 90° is known as an obtuse-angled triangle. 

Obtuse Triangle

In the above figure ∠STU = 120°. Thus, ∆STU is an obtuse-angled triangle.

3. Right Triangle:

A triangle whose one angles is a right angle (that is 90°) is called a right angled triangle or right angle.

In other words, a triangle in which any one of the three angles is exactly 90°, is known as a right-angled triangle. 

Right Triangle

In the above figure ∠PQR = 90°. Thus, ∆PQR is a right-angled triangle.


Questions and Answers on Classification of Triangle:

I. Fill in the blanks:

(i) The triangle with equal sides is …………………….

(ii) A ……………………. triangle has all sides of different length.

(iii) Each angle of equilateral triangle is …………………….

(iv) An ……………………. triangle has two equal sides.

(v) In obtuse angled triangle one angle is ……………………. 90°.

(vi) Each angle of an acute triangle is ……………………. than 90°.


Answers:

(i) Equilateral

(ii) Scalene

(iii) Equal

(iv) Isosceles

(v) Greater than

(vi) Less than


II. Classify the following triangle:

(i) Sides of triangle are 4 cm, 4 cm and 7 cm

(ii) Angles of triangle is 90°, 60° and 30°

(iii) Angles of triangle is 110°, 40° and 30°

(iv) Sides of triangle are 5 cm, 13 cm and 12 cm

(v) Angles of triangle is 60°, 60° and 60°


Answers:

(i) Isosceles triangle

(ii) Right-angled triangle

(iii) Obtuse-angled triangle

(iv) Scalene triangle

(v) Equilateral triangle

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