Let us learn how to construct a triangle if all the three sideslengths of the triangle are known.
Procedure to construct a triangle:
Let us constructs a \(\Delta ABC\)(say) with sidelengths \(x \ cm\), \(y \ cm\), and \(z \ cm\).
Step - 1: Construct the base line segment \(AB\) with one of the side lengths. Let us choose \(AB = x \ cm\).
Step - 2: With \(A\) as the centre, construct a sufficiently long arc of radius \(y \ cm\).
Step -3: Now, with \(B\) as the centre, construct a sufficiently long arc of radius \(z \ cm\), such that it intersects the previous arc at \(C\).
Step - 4: Join \(AC\) and \(BC\) to get the required triangle \(\Delta ABC\).
Example:
Construct triangles having the following sidelengths (all the units are in \(cm\)):
\(4, \ 6, \ 8\)
\(4, \ 6, \ 8\)
Step - 1: Construct the base line segment \(AB\) with one of the side lengths. Let us choose \(AB = 4 \ cm\).
Step - 2: With \(A\) as the centre, construct a sufficiently long arc of radius \(6 \ cm\).
Step -3: Now, with \(B\) as the centre, construct a sufficiently long arc of radius \(8 \ cm\), such that it intersects the previous arc at \(C\).
Step - 4: Join \(AC\) and \(BC\) to get the required triangle \(\Delta ABC\).
