**Construction of median of a triangle :**

Even though students know what is median, many students do not know, how to construct median of a triangle.

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

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

1. Ruler

2. Compass

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

Construct median to the side BC of the triangle ABC with AB = 6 cm, BC = 7 cm and AC = 5 cm.

Step 1 :

Draw triangle ABC using the given measurements.

Step 2 :

Construct the perpendicular bisector of the side BC to find midpoint E of BC.

Step 3 :

Now, join the vertex A and the mid point E of BC.

Now, AE is the median to the side BC of the triangle ABC.

This construction clearly shows how to draw median of a triangle with compass and straightedge or ruler. The median divides the side into two equal halves.

In the above example, median AE divides the side BC in to two equal halves.

From the steps of construction of median 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 "Construction of median of a triangle"

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