Congruence criterion with two sides and an angle known
SAS congruence criterion holds good if any two corresponding sides and the corresponding angles between those sides are the same.
Let us try to construct a congruent triangle using SAS congruence criterion.
Consider \(\triangle ABC\) with the dimensions as given in the figure below.
Figure 7.png
From the figure, it is understood that \(AB = 5\) \(cm\), \(AC = 4\) \(cm\), and \(\angle{CAB} = 60^\circ\).
Our aim is to construct a congruent triangle \(\triangle DEF\) using the \(2\) lengths and the angle 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, draw an line with an angle of \(60^\circ\).
Figure 8.png
Step \(3\): With \(D\) as radius and with \(4\) \(cm\) as radius, draw an arc on the line and mark the intersection as \(F\).
Figure 9.png
Step \(4\): Now join the point \(E\) and \(F\) to form the congruent triangle \(\triangle DEF\)
Figure 10.png