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.
Equilateral Triangle vs Isosceles Triangle
The main difference between an equilateral triangle and an isosceles triangle is that an equilateral triangle means that three sides polygon which have all the sides the same. On the other hand, an isosceles triangle is a triangle that has two same sides, and the measurement of the third side is different.
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 Between Equilateral Triangle and Isosceles Triangle
| 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
- 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.
- An equilateral triangle has all the angles constructed at 60 degrees. On the contrary, an isosceles triangle has only two similar angles.
- 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.
- 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.
- 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.
Conclusion
A triangle is a relatively prevalent shape in our environment. The word triangle is composed of two words: tri, which indicates three, and angle, referring to when two rays meet at the same point. So, it is a polygon having three angles.
It can be of three types, depending on the length of the sides. Equilateral triangles and isosceles triangles are distinct from each other. A right-angle triangle can never be an equilateral triangle since they have identical sides and angles. However, an isosceles can have one angle at 90 degrees when the other two angles are 45 each.
References
- https://www.tandfonline.com/doi/pdf/10.1080/0025570X.1997.11996515
- https://forumgeom.fau.edu/FG2016volume16/FG201632.ps