Isosceles Triangle Definition

It is one of three major types of triangles divided on the basis of their lengths. An Isosceles Triangle is one in which any two sides or arms are of equal lengths with equal corresponding angles.

Triangle is a specific term of Geometry that represents shapes with three sides and three angles. There are three major types of triangles used in Mathematics. All of those are distinguished mainly based on their side’s length.

Note:

You can read about Triangle here.

Real-life examples of Isosceles Triangle

There are different parts of daily routine equipment that make an isosceles triangle. Let us show you a few examples of them to have a better idea.

  • The base of a clothing hanger
  • The base of the guitar connected with its strings
  • Traffic controlling sign boards.

Amazing to know? You can also explore this type of triangle in many other products in your surroundings by using your creative thoughts.

Parts of an Isosceles Triangle

Like other shapes in Geometry, the Isosceles triangle also has three major parts. Let us show you briefly about those parts here.

Note:

Read about Axis in Geometry here.

  • Legs: The equal sides of an Isosceles triangle are collectively called the Legs of that particular Triangle.
  • Base: The third side of an Isosceles triangle is called the Base of the triangle. It can be larger or shorter than the legs of the triangle.
  • Vertex Point: It is a particular point of a triangle where both legs meet or join.

Note:

You can read about Vertex in detail here.

Types of Isosceles Triangle

No doubt, the Isosceles triangle is different from other major types depending on the length of the sides. But it also has three types further depending on the angles of the triangle.

  • Isosceles Acute Triangle: An Isosceles triangle having all three angles less than 90 degrees is called Acute Isosceles Triangle.
  • Isosceles Right Triangle: An Isosceles triangle having at least one angle of 90 degrees is called Right Isosceles Triangle.
  • Isosceles Obtuse Triangle: An Isosceles triangle with at least one angle greater than 90 degrees is called Obtuse Isosceles Triangle.

Basic operations on Triangles

As we all know that there are two major operations that can be performed on triangles i.e. Area calculation and Perimeter calculation. Let us show you how to find both of these for an Isosceles triangle

How to find the Area of an Isosceles Triangle?

To find the Area of the Isosceles Triangle, we have a specific formula. It is given below:

Area of an Isosceles Triangle = 1/2 (Base × Height)

Example 1:

Find the Area of an Isosceles Triangle with following measurements.

Height = 3 cm
Base = 12 cm

Solution:

To find the Area, we only have to put these values in the above formula.

Area = 1/2 (12 × 3)
Area = 1/2 (36)
Area = 18 square cm

How to find the Perimeter of an Isosceles Triangle?

Like Area, Isosceles triangle also has a specific formula to find the Perimeter. The formula is given below.

Perimeter of an Isosceles triangle = 2a + Base(b)
  • Here “a” represents the equal sides of the triangle.

Example 2:

Find the Parameter of the triangle with the following measurements.

a = 12 cm
b = 32 cm

Solution:

To find the Perimeter of an Isosceles triangle, we need to put the values in the above formula.

Perimeter = 2 (12) + 32
Perimeter = 24 + 32
Perimeter = 56 cm

Fun Facts about Isosceles Triangle

  • The sum of angles of an Isosceles triangle is 180 degrees. e.
  • The angles correspond to sides with equal lengths are also equal to each other.
  • An Isosceles right triangle has at least one angle of 90 degrees.
  • A right Isosceles triangle has two angles of 45 degrees.

Other Types of Triangles

Along with the Isosceles triangle, there are two other types. Let us tell you about them here briefly.

Note:

Read about Scalene Triangle here.

  • Scalene Triangle: It is a type of triangle having all three sides with different lengths. Such a triangle has all three angles of different measurements.
  • Equilateral Triangle:This type of triangle has all three sides of equal measurement. The angles in this triangle must be equal to each other.

Note:

Read about Area of an Equilateral Triangle here.

FAQ's

How to know if a triangle Isosceles or not?

If a triangle has two sides with equal lengths and two angles of equal measurement, it is said to be an Isosceles triangle.

What is the sum of angles in an Isosceles Triangle?

The sum of the angles of all triangles is 180 degrees.

Does an Isosceles Triangle have equal angles?

Yes, the sides with the same angles must have angles with the same measurements.

What are the three major types of the Isosceles Triangle?

An isosceles triangle has three major types mentioned below.

  • Acute Isosceles Triangle
  • Right Isosceles Triangle
  • Obtuse Isosceles Triangle
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