7. Construction of the Altitudes of a Triangle

The altitude of a triangle can be drawn from every vertex.

 

 

In the above \(\Delta ABD\), the perpendiculars \(AF\), \(BE\), and \(DC\) are altitudes from the vertices \(A\), \(B\), and \(D\) respectively.

Constructing the altitude precisely using just a ruler is not possible. To get a more precise angle of \(90°\), we use a set square along with a ruler.

 

We will learn the procedure to construct an altitude from one of the vertices of the triangle.

 

Let us construct a triangle \(ABC\) with \(BC = 5 \ cm\), \(AB = 7 \ cm\) and \(AC = 4 \ cm\). Construct an altitude from \(A\) to \(BC\).

 

 

Step 1: Construct a base line segment \(BC = 5 \ cm\).

 

 

Step 2: With \(B\) as centre and \(7 \ cm\) as radius, draw an arc.

 

 

Step 3: With \(C\) as centre and \(4 \ cm\) as radius, draw an arc which cuts the previous arc at \(A\).

 

 

Step 4: Join \(AB\) and \(AC\).

 

 

Step 5: Keep the ruler aligned to the base. Place the set square on the ruler as shown, such that one of the edges of the right angle touches the ruler.

 

 

Step 6: Slide the set square along the ruler till the vertical edge of the set square touches the vertex \(A\).

 

 

Step 7: Draw the altitude to \(BC\) through \(A\) using the vertical edge of the set square.