Angle A is using the reflective property... prove ΔABC ~ ΔADE by AA similarity postulate using a transformation triangles ABC and ADE, in which point D is between points A and B and point E is between points A and C
Translate triangle ADE so that point D lies on point B to confirm ∠D ≅ ∠B.
Translate triangle ADE so that point B lies on point E to confirm ∠B ≅ ∠E.
Dilate ΔABC from point A by the ratio segment AD over segment AB to confirm segment AD ~ segment AB.
Dilate ΔABC from point A by the ratio segment AE over segment AC to confirm segment AE ~ segment AC.