Isosceles Triangle

A triangle is a two-dimensional geometric shape that is made of three line segments connected to each other at endpoints. Triangles are classified on the basis of the sides and angles. A triangle that has two sides of equal measure and the third one of a different length is called an Isosceles Triangle. Triangle is a polygon that has three sides and three vertices. Moreover, the angles opposite to the equal sides are also equal in an isosceles triangle. Read this article to find all the information regarding the Isosceles Triangle. Here, in this article, we will discuss everything such as definition, properties, perimeter, area, solved examples and more.

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Isosceles Triangle

Isosceles Triangle, a triangle that has two equal sides. Also, the angle opposite the equal sides is also equal. In other words, when two sides of a triangle are equal, it is called an Isosceles Triangle.

Let △ABC be an Isosceles Triangle as shown in the image below:

The two equal sides of the triangle are called ‘Leg’. Whereas, the third side (which is not equal to the other two) is called ‘Base’. In the figure above AB and AC are legs and BC is the base.

AB = AC ≠ BC

Also, the sides opposite to

Triangle are equal.

∠B = ∠C ≠ ∠A

Properties of Isosceles Triangle

Some of the characteristics of Isosceles triangles and the rules are as follows. The properties includes:

Two sides of the Triangle are equal and are known as ‘Legs’.
The angles opposite to the two equal sides of the triangle is always equal.
The altitude of an Isosceles Triangle is measured from the base to the topmost vertex (angle made by the two legs) of the triangle.
A right isosceles triangle has a third angle as 90 degrees.
The angle made by the two equal sides of an isosceles triangle is known as the Vertex angle.
The angle which involves the base of the triangle is known as the ‘base angles’.
With the knowledge of anyone angle, the other two angles can be calculated as we know that the sum of angles in a triangle is 180 degrees (as per the properties of triangle).

Perimeter of Isosceles Triangle

The perimeter of a triangle is the sum of the length of all three sides. For this triangle the perimeter can be found using the length of the base and side. The formula to calculate the perimeter of the isosceles triangle is given by:

Perimeter of Isosceles Triangle = Sum of Length of two equal sides + Length of the other unequal side

If, ‘a’ is the length of the equal sides (legs) and ‘b’ is the length of the unequal side (base).

Perimeter of Isosceles Triangle (P) = 2a + b units

Area of Isosceles Triangle

The area occupied by the Isosceles Triangle in the two-dimensional space is called the area of the Isosceles Triangle. The area of a triangle is half the product of the base and height. For Isosceles Triangle, the area is given by:

A = ½ × b × h Square units

Where ‘b’ is the base and ‘h’ is the height.

Types of Isosceles Triangle

Isosceles Triangle are classified into different types namely,

Isosceles acute triangle
Isosceles right triangle
Isosceles obtuse triangle

Note that, based on the angle made by the two equal sides of an Isosceles Triangle, the triangles are classified as Isosceles acute, Isosceles right and Isosceles obtuse triangle.

Let’s go through the three different types of Isosceles triangle from below:

Isosceles Acute Triangle. The Isosceles Triangle in which the two legs (equal sides) make an angle less than 90 degrees is called an Isosceles Acute Triangle.

Isosceles Right Triangle: The Isosceles Triangle in which the two equal sides of the triangle make an angle of 90 degrees is called an Isosceles Right Triangle.
As it is a right angles triangle, we can apply the Pythagoras theorem. Let the sides of the right isosceles triangle are a, a, and h. Where a is the two equal sides and h is the hypotenuse.

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