Types of Triangles and Their Significance

Omar Khayyam, a Persian mathematician, and Chia Hsien, a Chinese mathematician, discovered the triangle thousands of years ago. The triangle is also described in a Saint Emmeram document from the 10th century that is well preserved at the Monaco library.

Pascal, a French mathematician, is credited with inventing a variety of triangle kinds, features, and uses. As previously said, we will now explore the fundamental forms of triangles.

Along with examining the definition of triangles, let’s discuss the types of triangles. 

Types of Triangles

Equilateral triangles, isosceles triangles, scalene triangles, right triangles, and oblique triangles are the five various types of triangles in geometry. Each one has its own unique shape, qualities, and formulas, which are detailed below.

1. Equilateral Triangle

Three equal sides make up an equilateral triangle, which means they have the same sides and angles. 

Because the angles of each side are identical, any triangle’s interior angles sum up to 180 degrees, making each angle 60 degrees.

The total degrees may simply be divided by three because the equilateral triangle contains three equal angles. As a result, each of an equilateral triangle’s angles is 60 degrees, resulting in an acute triangle.

2. Isosceles Triangle

Because an isosceles triangle has two equal sides, two of its angles are also equal. The isosceles triangle’s base is shorter, while the other two sides are similar in length.

The third angle can be determined by measuring either of the two angles. Isosceles triangles are sharp triangles since the maximum angle they can have is less than 90 degrees.

3. Scalene Triangle

A scalene triangle has radically different side lengths and measurements than a regular triangle. In other words, none of the scalene triangle’s sides are the same.

Other various types of triangles usually add up to 180 degrees, but the inner angles of a scalene triangle are not the same. A scalene triangle, for example, has 40 degrees, 50 degrees, and 90 degrees of angles that are all different from one another.

4. Right Triangle

This sort of triangle, often known as the right-angled triangle, has one of its inner angles at 90 degrees. Because it encompasses the study of the features of right triangles and the Pythagoras theorem, it features prominently in several fields of maths, such as trigonometry.

5. Oblique Triangle

Oblique triangles are further divided into two types:

·       Acute Triangle

An acute triangle is a triangle with three angles that are less than 90 degrees, just as an acute angle is an angle that is less than 90 degrees.

·       Obtuse Triangle

A triangle with an angle greater than 90 degrees is called an obtuse triangle. This indicates that the other two angles must be less than 90 degrees for the total to equal 180 degrees.

Properties of Triangle

The properties of properties are based on the sides and angles, as previously stated. Let’s have a look at some of the triangle qualities below:

Angle Sum Property

The total of a triangle’s three angles is 180 degrees or two right angles, known as the angle sum property of a triangle.

Properties of a Triangle:

The following are the properties of triangles:

• Angle Sum Property: All three inside angles add up to 180°. Consider the triangle ΔABC, where ΔABC, ∠A+ ∠B+ ∠C= 180° and the internal angles of the triangle are more than 0° and less than 180°
• A triangle is made up of three sides, three vertices, and three angles
• Exterior angle property: The total of a triangle’s Interior opposing and non-adjacent angles equals the triangle’s Exterior angle (also referred to as remote interior angles)
• The total of the lengths of any two triangle sides is always greater than the length of the third side. AB+ BC> AC, for example, or BC+ AC> AB
• The greatest side of the triangle is the side opposite the largest angle. The longest side of a right-angled triangle, for example, is the side opposite 90°
• A figure’s perimeter is determined by the overall length of the figure. As a result, the perimeter of a triangle is equal to the total of the lengths of the triangle’s three sides. ΔABC= (AB + BC + AC)
• The length difference between any two sides is always less than the length difference between the third and fourth sides. AB-BC< AC or BC-AC< AB, for example
• For similar triangles, the angles of the two triangles must be identical, and the corresponding sides must be proportional
• Area of a triangle: 1/2× base × height

Conclusion

The features of a triangle make it simple to recognise a triangle among a group of figures. A triangle is a three-sided polygon with three vertices and three angles. Triangles can be classed into many varieties based on the length of the sides and the angle measurements. Although all triangles share some qualities, there are a few that are exclusive to their sides and angles.