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An Overview on Isosceles and Equilateral Triangle

A triangle is nothing but a three-sided polygon which has three vertices along with three angles on each side. There are three types of triangles based on the sides such as equilateral triangles, isosceles triangle and scalene triangle. 

An isosceles triangle has two equivalent sides, the two sides of this triangle have equal length, and the remaining side features a different length. The name isosceles derived from the Greek words iso (same) and Skelos (leg). An isosceles triangle has two similar sides along with two identical angles. It also has a minimum of two congruent sides, also known as the legs, and the other side is called the base.

Isosceles Triangle

In an isosceles triangle, the angle between the base and those corresponding sides known as base angles and the angle created by two legs is the vertex angle. Isosceles triangle satisfies the theorem if the two sides of a triangle are similar, then the angle opposite to the sides are also same. An isosceles triangle can be categorized into an isosceles acute triangle, isosceles right triangle and isosceles obtuse triangle. 

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Isosceles Acute Triangle

The isosceles triangle can be acute if the two angles opposite to their concerning legs are equal and less than 90 degrees. 

Isosceles Right Triangle

A right isosceles triangle has two equal sides, whereas one of the two equal sides are perpendicular, and the other one act as the base. The unequal side is also known as hypotenuse, and it can be defined as 

h = √(a2 + a2) = √2a2 = a√2

or h = √2 a

Isosceles Obtuse Triangle

An obtuse triangle is a triangle in which one of its angles is greater than 90 degrees. An obtuse triangle can be a scalene triangle or isosceles triangle. 

Isosceles Obtuse Triangle

Equilateral Triangle 

An equilateral triangle has three equal sides and, therefore, three equal angle measures of 60 degrees. It is also known as a special type of isosceles triangles. Equilateral triangles satisfy the angle sum property of a triangle, and it is made up of two words such as equi means equal and lateral means sides. It is also called a regular polygon or even a regular triangle with three equal sides. Suppose ABC is an equilateral triangle, then we can define it as AB=BC=AC.

The centroid of an equilateral triangle is the centre of the triangle, and it is quite easy to find the centroid because all the sides of such a triangle are equal in length. On the other hand, the circumcenter of an equilateral triangle is the point of connection perpendicular bisectors of the sides. The circumcenter of an equilateral triangle goes through all three vertices of the triangle. So we can say when the in centre or centroid coincides with the circumcenter of a triangle, it is known as an equilateral triangle. 

area of Equilateral Triangle

FAQs on Isosceles and equilateral triangles 

How to calculate the area and perimeter of an isosceles triangle?

The area of an isosceles triangle is half the product of the base along with the height of the isosceles triangle. The formula used for calculating the area of an isosceles triangle is A= 1/2x b x h Square units. On the other hand, a perimeter in the shape of the boundary of the triangle and in an isosceles triangle is the sum of the three sides. The formula to calculate the perimeter of the isosceles triangle is P = 2a + b units, where a is the length of two equal sides and b is the base of the triangle. 

base angles theorem

Key Facets of Isosceles and Equilateral Triangle Assignment Help

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