Answer:
[tex]\triangle ADE \cong \triangle ACB[/tex] by SAS.
Step-by-step explanation:
From the graph, we see that [tex]\triangle ADE \cong \triangle ACB[/tex] by SAS, because [tex]AE \cong AB[/tex], [tex]AD \cong AC[/tex] and [tex]\angle EAD \cong \angle BAC[/tex], so by this given elements, we use Side-Angle-Side postulate.
To demonstrate the congruence between angles, we know by given
[tex]m\angle EAC = m\angle BAD[/tex]
By sum of angles, we have
[tex]\angle EAC=\angle EAD+\angle DAC\\\angle BAD=\angle BAC+\angle DAC[/tex]
Replacing this sum of angles in the first expression, we have
[tex]\angle EAD + \angle DAC = \angle BAC + \angle DAC\\\therefore\angle EAD = \angle BAC[/tex]
So, by SAS, [tex]\triangle ADE \cong \triangle ACB[/tex]
