**Construction of centroid of a triangle :**

Even though students know what is centroid, many students do not know, how to construct 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.

Here we are going to see "How to construct centroid of a triangle"

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 any 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.

From the steps of construction of centroid of a triangle, first we have to know, how to construct perpendicular bisector.

So, let us see, how to construct perpendicular bisector.

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. Since this bisects, it finds the midpoint of the given line segment.

**Key Concept - Perpendicular Bisector**

The line drawn perpendicular through the midpoint of a given line segment is called the perpendicular bisector of the line segment.

After having gone through the stuff given above, we hope that the students would have understood the stuff, "How to construct centroid of a triangle"

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