Congruence criterion with all \(3\) sides known
SSS congruence criterion holds good if all \(3\) corresponding sides of the triangles are the same.
Now let us try to construct a congruent triangle using SSS congruent criterion.
Consider \(\triangle ABC\) with the dimensions as given in the figure below.
Figure 2.png
From the figure, it is understood that \(AB = 5 cm\), \(BC = 7 cm\), and \(AC = 4 cm\).
Our aim is to construct a congruent triangle \(\triangle DEF\) using the \(3\) lengths acquired from the figure.
Step \(1\): Draw a line segment \(\overline{DE}\) of length \(5\) \(cm\).
Figure 3.png
Step \(2\): With \(D\) as centre and with \(4\) \(cm\) as radius, draw an arc.
Figure 4.png
Step \(3\): With \(E\) as centre and with \(7\) \(cm\) as radius, cut the already drawn arc and mark the intersection as \(F\).
Figure 5.png
Step \(4\): Now draw the line segments \(\overline{DF}\) and \(\overline{EF}\) to form the congruent triangle \(\triangle DEF\).
Figure 6.png