Equilateral Triangle: Overview, Questions, Preparation

There are three types of triangles, according to the length of the side of the triangle. They are equilateral triangle, isosceles triangle and scalene triangle. Among these, the equilateral triangle is what may be called a regular triangle. All sides of an equilateral triangle are equal to each other.

Properties of Equilateral Triangles

All equilateral triangles have several common properties. These properties include: 

1. All sides of an equilateral triangle are equal.
2. The sum of the interior angles of an equilateral triangle is 180º. The total of the exterior angles of an equilateral triangle is 360º.
3. All interior angles of an equilateral triangle have the same measure. This is equal to 60º.
4. The median and the altitude of an equilateral triangle are the same straight line, extending from a vertex to the centre point of the opposite side of the triangle.
5. The orthocentre of an equilateral triangle and the centroid of an equilateral triangle are the same point.

Equilateral triangle is a seemingly easy topic, but it is a significant one in higher classes. Hence, this topic is always taught in great detail, and students are encouraged to learn the properties of an equilateral triangle by heart. More than one class is generally devoted to teaching concepts of equilateral triangles.Equilateral triangles help  students understand lucidly about the sides, angles, orthocenter, centroid, altitude, and median of triangles using a regular shape.

Students are bound to meet equilateral triangles in classes X, XI, and XII, though, not as a geometric concept but as a trigonometric concept. In the chapter on mensuration, the area, perimeter, and other properties of an equilateral triangle are introduced to students. These properties are further reinforced through trigonometry and allied topics. From the examination point of view, it is important to learn the properties of equilateral triangles. Additionally, students should learn the formulae related to equilateral triangles such as its area, perimeter, etc. . They can appear in the examination for up to 2 marks.

1. What is the area of an equilateral triangle of side 4?

Solution.
The area of an equilateral triangle is √3a²/4. Here, a is the side of the triangle. When a = 4, the area is √3 x 4 x 4 / 4 = 4√3.

2. What is the length of the altitude of an equilateral triangle of side 4?

Solution.

The altitude of an equilateral triangle is a√3/2. For a = 4, the length of the altitude is 2√3.

3. What is the internal angle of an equilateral triangle of side 4?

Solution.
The internal angle of an equilateral triangle is always 60º.

Q: What is the sum of the internal angles of an equilateral triangle?

Q: What is the sum of the external angles of an equilateral triangle?

Q: What is the relation between the altitude and median of an equilateral triangle?

Q: What is the relation between the centroid and orthocentre of an equilateral triangle?

Q: What is the formula for the area of an equilateral triangle?