Scalene Triangles - Based on degree of angles of a triangle, Based on Both Sides and Angles

In geometry, a triangle is the smallest polygon. It is a three-sided closed 2- dimensional figure. A triangle can be categorized on the basis of the length of its sides and its interior angles.

Triangles are categorized as

1. Based on the length of sides
   1. Equilateral triangle- A triangle that has all sides of equal length is known as an equilateral triangle.
   2. Isosceles triangle- A triangle that has two of its sides of equal length is known as an isosceles triangle.
   3. Scalene triangle- A triangle that has all the sides of different lengths is known as a scalene triangle.
2. Based on interior angles
   1. Acute triangle- The triangle that has interior angles as acute angles.
   2. Obtuse triangle- The triangle that has one of its angles as an obtuse angle.
   3. Right triangle- The triangle that has one of its angles right angle.

Scalene triangle

A scalene triangle is one that has sides of different lengths. No two sides of a scalene triangle are the same. Since all the sides are of different measurements, the angles corresponding to different sides are also different. This is because angles opposite to unequal sides are also unequal. For example,

IMAGE

ABC is a scalene triangle with sides AB, BC and CA such that

AB ≠ BC ≠ CA

Also

∠ABC ≠ ∠BCA ≠ ∠CAB

Properties of a scalene triangle

1. All the sides of a scalene triangle are different from each other.
2. All the angles of a scalene triangle are different.
3. A scalene triangle does not have a line of symmetry. This means that such a triangle cannot be divided into two equal parts by a straight line.
4. A scalene triangle can be acute-angled, obtuse-angled or right-angled.
5. A scalene triangle follows the angle sum property of a triangle.
6. If a scalene triangle is acute-angled, the circumcenter lies inside the triangle and if obtuse-angled, then the circumcenter lies outside the triangle.

The perimeter of a scalene triangle

The perimeter of a scalene triangle is the measurement of the boundary of the triangle. It can be calculated by adding the length of its sides.

Perimeter of scalene triangle = a + b + c

Where a, b and c are the unequal sides of a scalene triangle. For example,

In the above figure, XYZ is a scalene triangle. The perimeter of the scalene triangle XYZ is Perimeter of scalene triangle XYZ = XY + YZ + ZX

Area of a scalene triangle

The area of a scalene triangle is the space occupied by that triangle in the plane. It can be calculated by two methods:

Method 1: By using height and base

If the height or altitude and base is given for a scalene triangle then the area is

Area = ½ . base. height

Method 2: By Heron’s formula

If the sides of the scalene triangle are given, the area can be calculated using Heron’s formula:

Area = √[s.(s-a).(s-b).(s-c)]

Where a, b and c are sides of the triangle and s is the semi perimeter.