Question

In the given figure, $\angle 1=\angle 2$ and $\angle 3=\angle 4$
Is $\Delta ADC\cong \Delta ABC$? Why?
Show that AD = AB and CD = CB
[3 marks]

Answer 1

In $\Delta ADC$ and $\Delta ABC$, $\angle 1=\angle 2$ [given]
AC = AC [common side]
$\angle 3=\angle 4$ [given]
[1 mark]
By ASA congruence criterion, $\Delta ADC\cong \Delta ABC$
[1 mark]

AD = AB [by CPCT]
CD = CB [by CPCT]
[1 mark]