Page 163 - Start Up Mathematics_7

10 Properties of Triangles

Consider the frame of a bicycle. Have you ever wondered why its frame is triangular in shape rather
than a quadrilateral? Triangle unlike quadrilateral or pentagon is rigid and cannot be deformed.
Because of this property, architects use triangles in the designs of bridges and other structures for

strength and stability.
The properties of triangles are also used by the Global Positioning System (GPS), which is a

navigation system that uses the properties of triangles to find the exact location of the users.
A
Let’s recall the definition of a triangle and its parts.
A triangle is a simple closed curve formed by three line segments.
∆ ABC has three sides AB, BC and CA. Further ∠ABC, ∠BCA

and ∠CAB are its three angles. A, B and C are its three vertices.
B C
Fig. 1
The three sides and three angles of a triangle are collectively known as elements of the triangle.

Classification of Triangles According to Sides

(i) Scalene triangle

A triangle having no two sides equal is known as a scalene triangle. In other words, in a
scalene triangle all the sides are different (Fig. 1).

(ii) Isosceles triangle

A triangle having any two sides equal is known as an isosceles
triangle (Fig. 2).
Fig. 2

(iii) Equilateral triangle

A triangle having all the three sides equal is known as an equilateral
triangle (Fig. 3).
Fig. 3
Classification of Triangles According to Angles
A
(i) Acute-angled triangle

A triangle having all angles acute is known as an acute-angled
triangle.
B C