Congruence criterion with two angles and one side known
ASA congruence criterion holds good if any two corresponding angles and the corresponding side between those angles are equal.
Let us try to construct a congruent triangle using ASA congruence criterion.
Consider \(\triangle ABC\) with the dimensions as given in the figure below.
Figure 11.png
From the figure, it is understood that \(AB = 5\) \(cm\), \(\angle{CAB} = 60^\circ\), and \(\angle{ABC} = 40^\circ\).
Our aim is to construct a congruent triangle \(\triangle DEF\) using the \(2\) angles and the length 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 \(E\) as centre, draw a line with an angle of \(40^\circ\) such it meets the already constructed line at \(F\). Now, the congruent \(\triangle DEF\) is formed.
Figure 12.png