AB = AC, < BAC = < DAE, ad = AE, BD = CE

AB = AC, < BAC = < DAE, ad = AE, BD = CE

It can be proved that the triangle bad is congruent with the triangle CAE, then BD = CE is obtained

Known: as shown in the figure, ab = AC, ad = AE, ∠ BAC = ∠ DAE, verification: BD = CE

It is proved that: in ∵ bad and △ CAE, ad = AE, bad = caeab = AC, bad = SAS and BD = EC

As shown in the figure, ab = AC, ad = AE, BD = CE are known

Proof
∵AB=AC,AD=AE,BD=CE
≌ Δ bad ≌ Δ CAD (three sets of congruent triangles with equal opposite sides)
∴∠BAD=∠CAD
∠BAC=∠BAD+∠DAC
=∠CAD+∠DAC
=∠DAE
That's it!