CONSTRUCTION OF CENTROID OF A TRIANGLE

Key Concept - Centroid

The point of concurrency of the medians of a triangle is called the centroid of the triangle and is usually denoted by G.

Before we learn how to construct centroid of a triangle, first we have to know how to construct perpendicular bisector of a triangle. 

So, let us learn how to construct perpendicular bisector.

Construction of Perpendicular Bisector of a Line Segment - Steps

To construct a perpendicular bisector of a line segment, you must need the following instruments.

1. Ruler

2. Compass

The steps for the construction of a perpendicular bisector of a line segment are :

Step 1 :

Draw the line segment AB. 

Step 2 :

With the two end points A and B of the line segment as centers and more than half the length of the line segment as radius draw arcs to intersect on both sides of the line segment at C and D.

Step 3 :

Join C and D to get the perpendicular bisector of the given line segment AB.

In the above figure, CD is the perpendicular bisector of the line segment AB.

This construction clearly shows how to draw the perpendicular bisector of a given line segment with compass and straightedge or ruler.

This bisects the line segment (That is, dividing it into two equal parts) and also perpendicular to it. 

Now, let us see how to construct the centroid of a triangle. 

Constructing Centroid of a Triangle - Steps

To construct centroid of a triangle, we must need the following instruments.

1. Ruler

2. Compass

Let us see, how to construct centroid of a triangle through the following example.  

Construct the centroid of the triangle ABC whose sides are AB = 6 cm, BC = 7 cm and AC = 5 cm.

Step 1 :

Draw triangle ABC using the given measurements. 

Step 2 :

Construct the perpendicular bisectors of two sides AC and BC to find the mid points D and E of AC and BC respectively .

Step 3 :

Draw the medians AE and BD and let them meet at G.

Now, the point G is the centroid of the given triangle ABC. 

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