Construction of Altitudes of a Triangle :
In this section, you will learn how to construct altitudes of a triangle.
Key Concept - Altitude of a Triangle
In a triangle, an altitude is the line segment drawn from a vertex of the triangle perpendicular to its opposite side.
To construct a altitude of a triangle, we must need the following instruments.
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 3 :
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 important application of altitudes of a triangles is to get orthocenter.
The point of concurrency of the altitudes of a triangle is called the orthocenter of the triangle and is usually denoted by H.
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.
After having gone through the stuff given above, we hope that the students would have understood how to construct altitudes of a triangle.
Apart from the stuff give in this section, if you need any other stuff in math, please use our google custom search here.
You can also visit our following web pages on different stuff in math.
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
Converting customary units worksheet
Customary units worksheet
Integers and absolute value worksheets
Nature of the roots of a quadratic equation worksheets
Trigonometry heights and distances
MATH FOR KIDS
Word problems on linear equations
Trigonometry word problems
Word problems on mixed fractrions
Converting repeating decimals in to fractions