# Altitude Definition

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```					                            Altitude Definition
Altitude Definition

The term altitude has different definitions or the meanings with reference to the different kinds
of the theories. Altitude is actually the term of the mathematics which most of us refer to as the
height. The altitude in every situation is found out to be perpendicular to that of the base.

Let us discuss the meaning of the term altitude with reference to a triangle. The altitude in the
case of a triangle is defined as the perpendicular distance from one of the side of the triangle
or from the extension of the side of the triangle to the vertex of that triangle which is opposite
to that side.

Also the altitude of any triangle is very helpful in calculating the area of that triangle. The
formula which we use very commonly to calculate the area of the triangle is equal to half
multiplied by the base of the triangle multiplied by the height of that triangle.

In this formula mentioned in the previous line the height is nothing but the altitude of the
triangle or we can say that it is the perpendicular distance starting from the base of the
triangle and ending at the vertex opposite to the base of that triangle.

Know More About :- Principle of Mathematical Induction

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It should also be noticed here that in the case of a triangle the base may be any one side of
the triangle and it is not necessary that it should be the side which is drawn at the bottom.

Thus to find the area of any triangle we can consider any one side of the triangle as the base
and after that the altitude which is at the right angle to the base is measured and these values
are put in the formula given below.

Area of the triangle = ( 1 / 2 ) * base * altitude

The definition of the altitude can also be framed in another way. The altitude is regarded as a
line that passes through any vertex of the triangle and which intersects the side opposite to
that vertex at the right angle.

It should be known that a triangle has 3 altitudes. Also there is one very interesting thing about
these 3 altitudes of the triangle that is all the 3 altitudes of any triangle pass always through
one common point which is known as the orthocenter of that triangle.

Now we have understood the meaning of the term altitude with respect to a triangle so let us
now have a look on the definition of the altitude with respect to any trapezoid or any
parallelogram.

In the case of a trapezoid or in the case of a parallelogram the altitude is defined as the
distance measured from the one side of that figure or it can be from the extension of the side
of that figure to the opposite side of that figure.

Because the altitude should always be perpendicular to that of the base it is generally used for
such types of the figures that do not possess a right angle.

For example the figures like the right triangles, the squares and the rectangles that already
possess a right angle do not need an altitude as the height in these cases is one of their
sides.

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For construction of base and altitude we have to follow some steps which are given below:

Step1: First we take two lines segment PQ and RS which defines the base length and altitude
of a triangle.

Step2: Then we draw a Point ‘A’ which becomes one end of the base of a triangle.

Step3: Now place the compass on point ‘R’ and measure the length ‘RS’ of the base of a
triangle.

Step4: with the help of compass draw an arc from point ‘A’.

Step5: Mark point ‘B’, and draw a line ‘AB’, this is the other end of triangle.

Step6: Now measure the base length with the help of compass and draw an arc on each side
of a base line from point ‘A’ and ‘B’.

Step7: We get the perpendicular bisector of the base which divides the base into two equal
parts.

Step8: Now measure the distance of Point ‘PQ’, this is the altitude of a triangle.

Step9: Then put the compass on the midpoint of the base line and draw an arc across the
perpendicular.

Step10: Then draw two sides AC and BC.

Step11: At last we get base and altitude of triangle.

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