Monday, 24 July 2017

Triangles III - How to Become Better With Centroid of a Triangle In 10 Minutes

In this post, we will discuss centroid of a triangle and properties of a triangle when it is cut by a median for SSC Exams. 

centroid of a triangle

Candidates who appear for competitive exams such as SSC Exams often get confused when the word Centroid is used. Centroid of a triangle is the point where all the mass of the triangle is concentrated. In our previous post, we have discussed different types of triangles and properties related to congruent triangles and similar triangles. In this post, we will discuss centroid of a triangle and its properties.
centroid of a triangle

What is a Median?

Before we understand about Centroid of a triangle, let's learn about the median.

Median Definition: Median is a line that connects the vertex of a triangle to the mid point of the opposite side of a triangle. 

If in a triangle ABC a median is drawn then the triangle ABC is divided into two equal halves.

AD is the Median
centroid of a triangle

 BE is the Median
centroid of a triangle

CF is the Median
centroid of a triangle


What is a Centroid of a Triangle?

Centroid of a triangle is a point where all the three medians of a triangle meet. 

Centroid of a triangle is denoted by the letter 'G.'
Centroid of a triangle always falls inside of a triangle. It never lies outside of the triangle. 


centroid of a triangle

Property 1: Centroid of a Triangle 

Centroid of a triangle always divides the median of a triangle in the ratio of 2:1

The 2 parts lie on the vertex side and the one part lies on the base side. 


centroid of a triangle

Property 2: Centroid of a Triangle 

Centroid of a triangle divides one triangle into three small triangles and these small triangles are 1/3 of the larger triangle. 


centroid of a triangle

Property 3: Centroid of a Triangle 

This property is based on the Apollonius Theorem. Apollonium theorem is named after a Greek astronomer and geometer Apollonius of Perga.

What is Apollonius Theorem?

Apollonius theorem states that "the sum of the squares of any two sides of a triangle is equal to twice the square of the half of the third side, together with twice the square on the median bisecting the third side".

For example: In a triangle ABC, if AD is the median then; 

centroid of a triangle

Property 4: Centroid of a Triangle 

In an equilateral triangle, all the three medians of a triangle are equal to each other. 

centroid of a triangle


In an isosceles triangle, only two medians of a triangle are equal to each other. 


centroid of a triangle


Hope it's now easier for you to attempt questions that are based on the centroid of a triangle.

Do write in the comments section below on how this post has helped you understand the properties of Centroid of a triangle asked in mock tests for SSC CGL. Also, download free questionnaire for practice!

Stay tuned for our next blog.
centroid of a triangle
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