Question
$\triangle\text{ABC}$ is isosceles with $AB = AC$. Line segment $AD$ bisects $\angle\text{A}$ and meets the base $BC$ in $D$. Is $\triangle\text{ADB}\cong\triangle\text{ADC}?$
✓
Answer
We have $AB = AC$ (Given) $\angle\text{BAD}=\angle\text{CAD}$ ($AD$ bisects $\angle\text{BAC}$ ) Therefore by $SAS$ condition of congruence, $\triangle\text{ABD}\cong\triangle\text{ACD}$
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