**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"

If you want to know more about "How to construct orthocenter of a triangle", please click here

If you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**