How Many Equal Sides does an Isosceles Triangle Have

Introduction

An isosceles triangle has 2 equal sides. The study of quality, shape, structure etc is called Maths. Maths deals with learning the logic behind a particular concept and then implementing it to solve daily real-life situations. Mathematics helps students to grow their problem-solving and logic-building skills. Generally, Maths includes four types of operators- addition, subtraction, multiplication, and division. Besides this Maths also includes various types of 2D and 3D shapes like rectangles, squares, triangles, circles, spheres, cuboids, cones, cylinders and many more. These all shapes help to define the outline or boundary of an object. Let’s learn about Triangles today.

Triangles

Triangle is a three-sided polygon i.e it has three sides or edges and three vertices. All the sides of a triangle can be either equal or different. We will be learning about the categorization of triangles based on their sides. A triangle also has three interior angles.

There is an important property known as Angle Sum Property which holds always true for the triangle to be formed. In case, the properties don’t hold it is impossible to construct the triangle.

Parts of a Triangle

The basic parts of a triangle are:

Vertices: It is a point where two sides meet. A triangle has three vertices. In the given below example A, B, and C are three vertices of the ∆ABC.

Sides: It is the line segment which joints two consecutive vertices of a triangle. In the given below example AB, BC, and CA are three sides of the ∆ABC.

Interior Angles: The angles that are formed from two consecutive sides of the triangle at the vertex where they converge. In the given below example, ∠A, ∠B, and ∠C or (α, β and γ) are three angles of the ∆ABC.

Exterior angles: The angle of one side that is formed with the exterior extension of the consecutive side. The given below example (θ) is the exterior angle of the ∆ABC. There can be three exterior angles possible in a triangle and they always sum up to 360 degrees.

Altitude: The altitude or height(h) of the triangle is the perpendicular distance drawn from the base of the triangle to the opposite vertex. In the given below example line drawn from vertex B to the opposite side AC is the altitude of the ∆ABC.

Categorization of Triangles on basis of Sides

Based on sides or edges, triangles are classified into three types:

Equilateral Triangles

Isosceles Triangles

Scalene Triangles

Let’s have a look at all these types of triangles.

Equilateral Triangles

A type of triangle which has all three sides equal in length to each other is called an Equilateral triangle.

For eg. Let’s say we have an ∆ABC, To be an equilateral triangle then all of its sides must be equal i.e AB = BC = CA

Also in the case of the Equilateral Triangle, all the interior angles are equal to 60 degrees.

Isosceles Triangles

A type of triangle in which two of its sides are equal in length is called Isosceles Triangle.

For example: Let’s say we have a ∆QPR, To be an Isosceles Triangle two of its sides must be equal in length (In this example PQ = PR = a)

Aso, In Isosceles Triangle the angle opposite to equal sides are also equal. This property of the Isosceles Triangle is called Isosceles Triangle Property.

Scalene Triangle

A type of triangle in which none of the sides of a triangle is equal in length is called Scalene Triangle.

For example, Let’s say we have ∆ABC, To be it as a scalene triangle none of its sides should be equal in length.

Also, In the case of the Scalene Triangle, all three interior angles are of different measures.

More details on Isosceles Triangle

• Isosceles Triangle is a type of triangle in which two sides are equal in length.

• The angles opposite to equal sides are also equal in measure.

• The height(h) of the isosceles triangle can be calculated by measuring the perpendicular distance drawn from the base of the triangle to the opposite vertex.

• The symmetry of an Isosceles triangle is the altitude or the perpendicular distance of the triangle.

Conclusion

Following points we had learnt:

• A triangle is a three-sided polygon.

• It has three vertices and three angles.

• The sum of all three interior angles of a triangle is equal to 180° and is called the Angle Sum Property of a triangle.

• There are three types of triangles based on sides that are Isosceles Triangle, Equilateral Triangle and Scalene Triangle.

• Equilateral Triangles are triangles which have all three sides and three angles equal.

• Isosceles Triangles are triangles which have two sides equal and angles opposite to equal sides are also equal.

• Scalene Triangle is a triangle which has all three sides and angles of different measures.

• Thus In the case of an Isosceles Triangle, we have two of its sides equal in length.