Question

In the adjoining figure. AB = AC and BD = DC. Prove that $\Delta ADB\cong \Delta ADC$ and hence show that
(i) $\angle ADB=\angle ADC$
(ii) $\angle BAD=\angle CAD$

Answer 1

Given $AB=AC,BD=DC$

In $△ADB,△ADC$

$AB=AC$

$BD=DC$

$AD=AD$

By $SSS$ congruency

$△ADB\cong △ADC$

$⟹\angle ADB=\angle ADC$

and also $\angle BAD=\angle CAD$