**Construction of orthocenter of a triangle :**

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

**Key Concept - Orthocenter**

The point of concurrency of the altitudes of a triangle is called the orthocenter of the triangle and is usually denoted by H.

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

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

1. Ruler

2. Compass

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

Construct triangle ABC whose sides are AB = 6 cm, BC = 4 cm and AC = 5.5 cm and locate its orthocenter.

Step 1 :

Draw the triangle ABC with the given measurements.

Step 2 :

Construct altitudes from any two vertices (A and C) to their opposite sides (BC and AB respectively).

The point of intersection of the altitudes H is the orthocenter of the given triangle ABC.

From the steps of construction of circmcenter, it is very clear, first we have to know, how to construct altitudes of a triangle.

So, let us see, how to construct altitudes of a triangle.

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

1. Ruler

2. Compass

The steps for the construction of altitude of a triangle.

Step 1 :

Draw the triangle ABC as given in the figure given below.

Step 2 :

With C as center and any convenient radius draw arcs to cut the side AB at two points P and Q.

Step 4 :

With P and Q as centers and more than half the distance between these points as radius draw two arcs to intersect each other at E.

Step 4 :

Join C and E to get the altitude of the triangle ABC through the vertex A.

In the above figure, CD is the altitude of the triangle ABC.

This construction clearly shows how to draw altitude of a triangle using compass and ruler.

As we have drawn altitude of the triangle ABC through vertex A, we can draw two more altitudes of the same triangle ABC through the other two vertices.

Therefore, three altitude can be drawn in a triangle.

The point of concurrency of the altitudes of a triangle is called the orthocenter of the triangle and is usually denoted by H.

After having gone through the stuff given above, we hope that the students would have understood "Construction of orthocenter of a triangle"

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