Page 176 - ICSE Math 7

A

2
The two interior angles opposite to an exterior angle are called its
interior opposite angles. In the adjoining figure, ∠1 is an exterior
angle and ∠2 and ∠3 are its interior opposite angles.
3 1
B
C D
Relation between an exterior angle and its interior opposite angles
A
The exterior angle of a triangle is always equal to the sum of its two
interior opposite angles. 2
Consider a DABC with its side CB produced to D to form an exterior
angle ABD. 1 3
∠ABD + ∠ABC = 180° (Linear pair) D B C
Also, ∠ABC + ∠BCA + ∠CAB = 180° (Sum of the angles of a triangle is 180°)
So, ∠ABC + ∠BCA + ∠CAB = ∠ABD + ∠ABC

⇒ ∠BCA + ∠CAB = ∠ABD
Thus, the exterior angle ABD is equal to the sum of its two interior opposite angles.

Classification of Triangles

Triangles can be classified in two ways:
(a) on the basis of the lengths of their sides (b) on the basis of the magnitudes of their angles

On the basis of sides

Isosceles triangle
A triangle in which any two sides are A Vertical
equal is known as an isosceles triangle. angle Maths Info
The third side is called the base and 3 cm 3 cm
the angles opposite to equal sides Base If a side is called the base of a triangle,
are known as base angles. The angle angles then the angle opposite to that side is
known as vertical angle.
C
opposite to base is known as vertical B 5 cm Base
angle.

Scalene triangle A
A triangle in which all the three sides are unequal is known as a scalene 3 cm 5 cm
triangle.
B C
4 cm

Equilateral triangle A
A triangle in which all the three sides are 4 cm Maths Info
equal is known as an equilateral triangle. 4 cm An equilateral triangle is always
isosceles but the converse is
not true.
B C
4 cm

162