Types of Triangles

Triangle is the most important topic in the geometry component of different competitive tests such as the CAT. Many triangle problems are dependent on fundamental ideas like understanding sides and angles, as well as a few basic triangle theorems.

It’s worth noting that the questions can be found on even the most basic principles. The focus of this paper will be on two triangle principles and their applications.

The triangle is a three-sided two-dimensional geometrical form. If we examine a triangle ABC and its three sides to be a, b, and c, side an is often thought to be the side opposite to angle A.

Triangle

A triangle is a two-dimensional closed shape with three sides, three angles, and three vertices. A triangle is a polygon as well.

Examples of Triangles

Sandwiches, traffic signs, fabric hangers, and a billiards rack are all examples of triangles in real life.

Non-examples of Triangles

Non-examples of triangles are shown above. These shapes are not triangles because –

• The first is a four-sided figure.
• An open shape is the second figure.
• A curved side is shown in the third figure.

Parts of Triangle

1. There are three sides to a triangle. The sides of the triangle ABC are AB, BC, and CA.
2. The angle of the triangle, indicated by the symbol, is the angle created by any two sides of a triangle. There are three angles in a triangle. ABC,BCA, and CAB are the three angles of the triangle ABC. These angles are also known by the letters B, C, and A.
3. The point of intersection of any two sides of a triangle is known as a vertex. A triangle has three vertices. In triangle ABC, the vertices are A, B, and C.

Properties of a Triangle

• The sum of a triangle’s three interior angles is always equal to 180°.
• The length of any two triangle sides added together is always bigger than the length of the third side.
• A triangle’s area is half of the product of its base and height.

Types of Triangle

Different sorts of triangles are categorised based on the length of their sides and the angles’ measurements. The triangle is a typical design that is utilised in building because of its stiffness and stability. Understanding these features allows us to apply the concepts to a variety of real-life situations.

Types of Triangles Based on Sides

Triangles are categorised into the following types based on their side lengths:

• Equilateral Triangle: When all three sides of a triangle are the same length, it is called an equilateral triangle.
• Isosceles Triangle: An isosceles triangle is formed when the two sides of a triangle are equal or congruent.
• Scalene Triangle: A scalene triangle is one in which none of the triangle’s sides are equal.

Types of Triangles Based on Angles

Triangles are categorised into the following types based on their angles:

• Acute Triangle: An acute-angled triangle or acute triangle is defined as a triangle with all of its angles measuring fewer than 90°.
• Right Triangle: A right-angled triangle or right triangle is one in which one of the angles is 90°.
• Obtuse Triangle: An obtuse-angled triangle, also known as an obtuse triangle, is one in which one of the triangle’s angles is more than 90°.

Area of Triangle

The area of a triangle is the area that it occupies in two-dimensional space. The area of various triangles varies depending on their size. We can calculate the area of a triangle by knowing its base length and height. It’s calculated in square units.

As a result, the area of a triangle is 12 (Product of base and height of a triangle)

The sides of the triangle are PQR, PQ, QR, and RP. The triangle’s base is QR, while the triangle’s height is PS. PS is perpendicular to the side QR from the vertex P. So, to calculate the area of PQR, we apply the formula:

Area ∆PQR=1/2 

Or, Area ∆PQR=1/2(QR×PS)

The Perimeter of a Triangle

The perimeter of a triangle is equal to the sum of the lengths of all its sides.

As a result, the triangle’s perimeter equals the sum of its three sides.

The perimeter of the triangle PQR is equal to the total of the three sides, PQ, QR, and RP.

So, Perimeter of ∆PQR=PQ+QR+RP.

Conclusion

The most essential issue in the geometry section of several competitive tests, such as the CAT, is the triangle. Many triangle problems need comprehension of basic concepts such as sides and angles, as well as a few basic triangle theorems.

It’s worth mentioning that the questions cover even the most fundamental concepts. Two triangle principles and their applications will be the subject of this paper.

The triangle is a two-dimensional geometric object with three sides.

 When we look at a triangle ABC with three sides a, b, and c, we frequently think of side an as the side opposite to angle A.