Equilateral Triangle vs Isosceles Triangle: Difference and Comparison

Mathematics is a vast aspect to comprehend. Under maths, the triangle is a well-known and easy concept to learn for making a career in the construction business and learning to calculate the measurement of mountains.

An equilateral triangle and an Isosceles triangle are two types of triangles that have distinct applications in real life. These topics are taught to children at the secondary level.

Key Takeaways

1. Equilateral triangles have three equal sides and angles, while isosceles triangles have two sides and two equal angles.
2. The interior angles of an equilateral triangle measure 60 degrees each, whereas the angles of an isosceles triangle depend on the length of the sides.
3. Equilateral triangles are a specific type of isosceles triangle, as they fulfill the requirement of having at least two equal sides.

Equilateral Triangle vs Isosceles Triangle

An equilateral triangle is a type of triangle in which all three sides are of equal length, and all three angles are of equal measure, i.e., 60 degrees.  An isosceles triangle is a type of triangle that has two sides of equal length and two angles of equal measure. The third side, called the base, is of a different length.

All sides of an equilateral triangle are the same length, and it lies in an equiangular position. Each angle of an equilateral triangle must be at 60 degrees.

Equilateral triangles are essential to the construction of traffic signals on highways. Moreover, edible triangular tortillas are also available in equilateral shapes.

The mathematician Euclid brought the concept of an isosceles triangle. This type of triangle has two sides of the same length and one side of a different length.

Similar sides of a triangle are known as the legs. However, a non-similar one is known as a base.

The slice of the Italian snack Pizza is served in an isosceles triangle shape.

Comparison Table

Parameters of Comparison	Equilateral Triangle	Isosceles Triangle
Definition	An equilateral triangle can be characterized as a triangle with the same size of sides.	An isosceles triangle has two sides that are similar in length and one side that is not.
Angle	An equilateral triangle is built at a 60-degree angle.	An isosceles triangle has two similar triangles and one non-similar angle.
Perimeter	The equilateral triangle’s perimeter formula is thrice the measurement of sides.	The isosceles triangle’s perimeter is twice the length of sides + base.
Area	The formula for calculating the equilateral triangle’s area is√3sides2/4.	The formula for calculating the isosceles triangle’s area is a product of base and height divided by 2.
Application	The traffic signals and edible tortillas are equilateral triangles.	The pizza slice is cut in an isosceles triangle shape.

What is Equilateral Triangle?

Since the 17th century, the triangle shape has been well-known, and it is named after a French mathematician. Later, triangles were divided into three parts; Scalene triangle, Isosceles triangle, and Equilateral triangle.

The equilateral triangle consists of two words: Equi, which means equal, and lateral, which means sides. As a result, an equilateral triangle is one with all equal sides.

Since the total sum of equilateral triangle angles is 180 degrees, each angle of the triangle is 60 degrees.

Moreover, when we draw a perpendicular from one side to the opposite corner, it bisects the triangle into two halves. The angle is also bisected into halves and becomes 30 degrees each.

The medians in the equilateral triangle are also the same.

For example, ABC is an equilateral triangle. So, AB= BC= CA.

The area of an equilateral triangle is √3a2/4.

Let AB=BC=CA= 8 cm= a,

So, the area of the equilateral triangle ABC = 16√3

The formula of the perimeter of an equilateral triangle = 3a

So, the perimeter of the equilateral triangle ABC= 3 x 8= 24

The equation of the height of an equilateral triangle = √3a/2

So the height of equilateral triangle ABC =4√3

After drawing the perpendicular from BC to corner A,

The area will be halved and will become= Area/ 2= 8√3

What is Isosceles Triangle?

An isosceles triangle is also one of the types of the three side polygon called a triangle. An isosceles triangle is when two of its sides are equal, and one side is different from the other.

The same sides are legs of a triangle, and the non-similar side is a base of an isosceles triangle.

The golden triangle whose angles are in ratio (1:1:3) is an example of an isosceles triangle. The golden triangle is also known as the sublime triangle.

The pizza slice is also is available in an isosceles triangle shape.

Egyptians and Babylonians in ancient times created such triangles. Buildings pediments and gables form an isosceles triangle.

The sum of the isosceles triangle is also 180 degrees. Moreover, opposite angles of the same sides are also equal.

For example, ABC is a triangle.

When AB = AC, then Angle B and Angle C are equal.

So the sum of the Isosceles triangle can be ∠A +∠B+∠C =180

∠A +2(∠B)= 180

The formula of area of isosceles triangle = 1/2 × b × h

h= perpendicular of triangle = 4

side = 4

base = 3

So Area = 6

Parameter = 2(sides) + base = 2 (4) + 3 = 11

Main Differences Between Equilateral Triangle and Isosceles Triangle

1. An equilateral triangle means all the lateral of the triangle are of equal length. On the other hand, an isosceles triangle means two lateral are the same, and the third is different.
2. An equilateral triangle has all the angles constructed at 60 degrees. On the contrary, an isosceles triangle has only two similar angles.
3. Traffic signals and tortillas are made with an equilateral triangle concept. On the other side, an isosceles triangle’s concept is present in the golden triangle.
4. A right-angle triangle can not be called an equilateral triangle. When two angles are 45 degrees, and the third is 90 degrees, this isosceles triangle is also a right angle triangle.
5. The formula for calculating the area of an equilateral triangle is √3 sides2/4. On the contrary, it is half the product of base X height in the case of an isosceles triangle.

References

1. https://www.tandfonline.com/doi/pdf/10.1080/0025570X.1997.11996515
2. https://forumgeom.fau.edu/FG2016volume16/FG201632.ps

Last Updated : 13 February, 2024