Classification of triangles on the basics of sides –
Scalene Triangle -
No two sides of a scalene triangle are equal. In the figure, ABC is a scalene triangle as AB ≠ BC ≠ CA
Isosceles Triangle –
An Isosceles triangle has two equal sides. In the figure, ABC is an isosceles triangle in which AB = AC (equal sides are marked by an equal number of strokes). The third side BC is called the base of the triangle, while ∠ABC and ∠ACB are called the base angles. ∠BAC is called the vertical angle.
The angles opposite to the equal sides of an isosceles triangle are equal.
In the figure, AB = AC,
So, ∠ABC = ∠ACB
The converse, or opposite, of this is also true. Thus, if two angles of a triangle are equal, the sides opposite to them are equal.
In the figure, ∠ABC = ∠ACB.
So, AB = AC
This also implies that the angles of a scalene triangle are all unequal.
Equilateral Triangle –
All the three sides of an equilateral triangle are equal. In the adjoining figure, ABC is an equilateral triangle as AB = BC = CA
All the angles of an equilateral triangle are equal.
In the figure, ∠BAC = ∠ABC = ∠ACB
If all the angles of a triangle are equal, it must be an equilateral triangle.
In the adjoining figure, ∠P = ∠Q = ∠R,
Hence, PQR is an equilateral triangle.