What is a triangle?
A triangle is a three-sided closed plane shape with three vertices and three angles. All sides of the triangle may or may not be of the same length. It is represented by the symbol ∆.
A triangle with three vertices, A, B, and C, is represented as ∆ABC.
Real-life examples of triangles
The most common examples of triangles in our daily lives are sandwiches, sailing boats, truss bridges, and the Bermuda Triangle.
Components of a triangle
A triangle is made up of several parts. It has three sides, three vertices, and three angles. Examine the triangle ABC below, which depicts a triangle’s sides, vertices, and interior angles.
Classification of triangles based on sides
We measure the length of each side of the triangle to classify it according to its sides. Triangles are classified as follows based on their sides:
Equilateral triangle:
All sides of an equilateral triangle are of the same length. In this case, each of the interior angles will measure 60 degrees. Because its angles are equal, an equilateral triangle is also known as an equiangular triangle. An equilateral triangle with all three sides measuring x units is represented in the diagram below.
Isosceles triangle:
In an isosceles triangle, at least two of the three sides are equal in length. In other words, an isosceles triangle has two sides and two angles that are equal in measure. An isosceles triangle is pictured in the diagram below.
AB = AC
Scalene triangle:
The lengths of the sides of a scalene triangle are all different. In such a triangle, no side will be equal in length to any of the other sides. In a scalene triangle, all of the interior angles are also different. A scalene triangle is pictured in the diagram below.
AB ≠ BC ≠ CA
Solved Examples
Example 1:
Classify the triangle based on its sides.
a.
Solution:
All the sides of the triangle are equal in length.
So, it is an equilateral triangle.
b.
Solution:
Two sides of the triangle are equal in length.
So, it is an isosceles triangle.
Example 2:
Classify the traffic sign according to its sides and then find the sign’s perimeter.
Solution:
The traffic sign is in the shape of a triangle with three sides that are equal in length.
As a result, the traffic sign is equilateral.
To determine its perimeter, find the sum of all the side lengths of the traffic sign.
20 + 20 + 20 = 60 [Add]
As a result, the perimeter of the traffic sign is 60 inches.
Example 3:
Classify the triangular park according to its sides and then determine the park’s perimeter.
Solution:
No sides in the triangular park are of the same length.
As a result, it’s a scalene triangle.
To determine its perimeter, find the sum of all the side lengths of the park.
90 + 60 + 40 = 190
As a result, the perimeter of the triangular park is 190 meters.
Example 4:
Classify the pizza slice according to its sides and then find its perimeter.
Solution:
A pizza slice is a triangle with two sides that are equal in length.
As a result, the pizza slice is isosceles.
To determine its perimeter, find the sum of all the side lengths of the slice of pizza.
15 + 15 + 10 = 40
As a result, the perimeter of the pizza slice is 40 meters.
Example 5:
Classify the triangle based on its sides.
Solution:
1. All the sides of the triangle are equal.
So, it is an equilateral triangle.
2. Two sides of the triangle are equal in length.
So, it is an isosceles triangle.
3. There are no sides in the given figure that are of the same length.
As a result, it’s a scalene triangle.
No. A triangle is a three-sided, two-dimensional shape.
A triangle with all of its sides equal in length is known as an equilateral triangle.
Based on its sides, a triangle is classified as follows:
1. Equilateral triangle
2. Isosceles triangle
3. Scalene triangle