Question 720830
You have to prove angle DEC is congruent to angle BAC 
( exterior angle theorem) 
angle DEC = angle DAE +EDA

But DAE =ADE=BAD ( given)

In triangles ABC & CED angle C is common angle.
DEC = BAC

Triangles are similar.

Take the ratio of sides ( basic proportionality theorem)

EC/AC = DC/BC

(AC-AE)/AC = (BC-BD)/BC

AC/AC  - AE/AC = BC/BC- BD/BC

1-AE/AC = 1- BD/BC

therefore AE/AC = BD/BC