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Triangles are polygons, which are enclosed on the three sides. It is known that triangles can be classified into three different types. They are Equilateral triangles, Isosceles triangles, and Scalene triangles.  These types have a very minimal difference, in terms of equality of the sides. 
  • Equilateral Triangles have all equitable sides, measuring the same
  • Isosceles Triangle has two sides equitable in nature
  • Scalene triangle has three sides that are unequal in nature
Let us look at the Isosceles triangle in detail.

Triangle: Isosceles?

One of the types of a triangle is called the Isosceles triangle. A triangle that has two equitable sides is commonly known as the Isosceles triangle. In simple terms, the length of any two sides of the triangle is equal in measure. It is a triangle whose two sides are congruent in nature.  To understand the concept of the Isosceles triangle, let us take up an activity. Initially, fold a piece of paper- which is rectangular in shape- in half. Now, try and mark a line starting from the top corner to the bottom edge. Now, unfold the sheet; you will get to see a figure which looks like a triangle. Mark the triangle vertices as A, B, and C. Now, use a scale to measure the sides AB and AC. When you find that the sides AB and AC are equal, you will get an Isosceles triangle. Since the isosceles triangle has congruent sides- the opposite angles of these congruent sides will also be considered equal.  Let us look at the equation for the calculation of the area of an isosceles triangle. 

Isosceles Triangle: Area

In a two-dimensional area, the region that is used by an isosceles triangle is defined as the Area of an Isosceles Triangle. It is the bisection of the outcome of the height and base of the isosceles triangle. This can be written as-  Area of an Isosceles Triangle = ((½)× Height × Base) square units.

Isosceles Triangle: Perimeter

The dividing line of a shape is popularly known as the Perimeter. Therefore, the perimeter of an isosceles triangle is the summation of all its three sides. It can easily be found in the side value and the base value is given. The perimeter can be written as-  Perimeter of an Isosceles triangle = (Side + Side + Base) units. Let us look at the properties of this type of triangle. 

Isosceles Triangles: Properties

The properties make the components and shape unique and distinct from one another in geometry. Some of the properties of the Isosceles triangle are-
  • Two sides of the triangle are equal
  • The opposite angles subtended by the equal sides are also equal
  • The base is the opposite side of the vertex angle. Therefore, the base angles and the base are equal in measure
  • The equal sides of the triangle are known as the legs and the angle subtended by these legs is known as the Apex angle. These are also known as the Vertex angles
  • The line drawn perpendicularly from the vertex angle intersects the base and vertex angle
  • The line drawn perpendicularly from the vertex angle splits the triangle into congruent triangles of two. This perpendicular line is commonly known as the line of symmetry

Isosceles Triangle: Angles

Like any other triangle, the angles in a triangle which is isosceles in nature have the sum of 180 degrees. As it is known that two angles and two sides of an isosceles triangle are equal. And, these two equal angles lie opposite the equal sides of the triangle. Therefore, one angle out of the three angles is unequal- the apex angle. As it is known that the angles can be of three types- acute, obtuse, and right angle. 
  • If all the three angles of the triangles are less than 90o and 2 of them are equal, then it is an isoceles acute triangle
  • If one of the angles of a triangle is is greater than 90o and the two other angles are equal, then it is an isoceles obtuse triangle
  • For a right isoceles triangle one of its angle will be 90o and the other 2 angles will be equal
Now, let us look at the difference between the three types of triangles. 

Table differentiating- Type of Triangle

Equilateral Triangles Isosceles Triangles Scalene Triangles
Lengthwise, all three sides of the triangle are equal. Lengthwise, the two sides are equal. Lengthwise, all three sides of the triangle are unequal.
The line drawn perpendicularly from the angle intersects the parent angle and the opposite side of that angle. The line drawn perpendicularly from the vertex angle splits the triangle into congruent triangles of two. There are no relations. 
The angles are equal in measure. Each angle in equilateral angles is 60̊. Two angles in Isosceles Triangle are equal. There exists one unequal angle.  The three angles of the Scalene triangle are unequal in nature and measure.