Question

In the figure, it is given that AE = AD and BD = CE. Prove that $△AEB$ is congruent $△ADC$.

Answer 1

We have $AE=AD$ and $CE=BD$.
Adding, we get $AE+CE=AD+BD$
$\Rightarrow AC=AB$.
In triangles $AEB$ and $ADC$, we have
$AE=AD$ ....... (given);
$AB=AC$ ....... (proved);
$\angle EAB=\angle DAC$, (common angle).
By SAS postulate $△AEB\cong △ADC$.