3. Construction of triangle using sides

Let us learn how to construct a triangle if \(3\) sides are known. To construct a triangle, first we shall draw a rough diagram which gives an idea where the sides would be. Let us consider an example.

Let us construct a triangle in which all sides are of length \(3 \ cm\).

 

 

 

Step 1: Construct the base \(AB = 3 \ cm\).

 

 

Step 2: With \(A\) as centre, draw an arc of radius \(3 \ cm\).

 

 

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

 

 

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

 

 

Thus, \(ABC\) is the required triangle.

 

Now, we know how to construct an equilateral triangle. Let us see the general construction of a triangle (scalene, isosceles and equilateral triangle).

Let us construct a triangle whose sides are \(5 \ cm\), \(7 \ cm\) and \(4 \ cm\).

 

 

 

Step 1: Let us construct the base \(AB\) of any length. Let us choose \(AB = 5 \ cm\).

 

 

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

 

 

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

 

 

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

 

 

Thus, \(ABC\) is the required triangle.