Angles ACB and ECD are equal. (Vertical angles are equal.)
Thus angles BAC and DEC are equal. (The sum of all the interior angles of a triangle is 180 degrees, so if two pairs of angles are the same in two triangles, so is the third pair.)
Now, angles DAE and BEA are equal. (Given)
Thus angles BAE and DEA are equal. (Equals plus equals are equal.)
So in triangles ABE and EDA we have that angles ABE and EDA are equal, angles BAE and DEA are equal, and angles BEA and DAE are equal.
Thus the triangles ABE and EDA are similar.
Oops! Not done yet.
We also have that side AE is equal to side EA. Since we have corresponding sides of similar triangles equal the two triangles ABE and EDA are congruent.