Page 175 - ICSE Math 7

16 Triangles

Key Concepts

• Triangle • Altitude and Medians of a Triangle
• Classification of Triangles • Pythagoras Property (or Pythagoras Theorem)
• 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 connot 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.

In this chapter, we will learn about triangles, classification of triangles on the basis of the lengths of
the sides and on the basis of magnitude of the angles. We will also learn about properties of triangles
and the pythagoras theorem.
A
Triangle
A triangle is a closed figure bounded by three line segments. The region
enclosed by a triangle is known as the triangular region. Symbolically, Triangular
a triangle ABC is denoted as DABC. region
B C
Sides

The line segments forming a triangle are known as its sides. In DABC, AB, BC and CA are its sides.
Vertices

A vertex is a point of intersection of any two sides of a triangle. In DABC, A, B and C are its vertices.
There is a relation between a side and a vertex. In DABC, A is the vertex opposite to side BC, B is the
vertex opposite to side CA and C is the vertex opposite to side AB.

Angles
The angle made by any two sides of a triangle is known as an
angle or interior angle of a triangle. For example, the interior A
angles of DABC are ∠ABC (or ∠B), ∠BCA (or ∠C) and ∠CAB 3 4
(or ∠A). When any side of a triangle is produced, the angle formed
outside the triangle is known as an exterior angle of the triangle.
If side AB is produced to D, ∠1 is formed. It is also known as an 2
5
exterior angle at B. If side CB is produced to E, ∠2 is formed. Also, E B C
∠1 = ∠2, being vertically opposite angles. So, there are two exterior 1 6
angles of equal magnitude at each vertex. Thus, on producing all D
the sides of a triangle, six exterior angles are formed.
Also, ∠1 = ∠2, ∠3 = ∠4, ∠5 = ∠6.

161