Question

In the figure 3.50 $\angle$DAC $\cong$$\angle$BCA find the missing information which is required and sufficient to prove $∆$ADC $\cong$ $∆$CBA by
(i) SAS test
(ii) SAA test
(iii) ASA test

Answer 1

$$\begin{gathered} \mathrm{Given}:\angle \mathrm{DCA}=\angle \mathrm{BCA} \\ \mathrm{We}\mathrm{know}\mathrm{that}\mathrm{CA}=\mathrm{CA}\left(\mathrm{common}\right) \\ \left(\mathrm{i}\right)\mathrm{AD}=\mathrm{BC} \\ \therefore △\mathrm{ADC}\cong △\mathrm{CBA}(\mathrm{SAS}\mathrm{test}) \\ \left(\mathrm{ii}\right)\angle \mathrm{ADC}=\angle \mathrm{CBA} \\ \therefore △\mathrm{ADC}\cong △\mathrm{CBA}(\mathrm{SAA}\mathrm{test}) \\ \left(\mathrm{iii}\right)\angle \mathrm{CAB}=\angle \mathrm{DCA} \\ \therefore △\mathrm{ADC}\cong △\mathrm{CBA}(\mathrm{ASA}\mathrm{test}) \end{gathered}$$