Question 703159
Looking at triangles ABC and ADC:
AC is congruent with itself.
So triangle ABC is congruent with ADC (Side-Side-Side congruency)
By CPCTC (Corresponding Parts of Congruent Triangles are Congruent),
angles BAC and DAC are congruent, making AC the bisector of angle BAD.
 
Looking at triangles ABE and ADE:
AE is congruent with itself.
AB is congruent to AD (given)
Angles BAE(=BAC) and DAE(=DAC) are congruent (proven above)
So triangle ABE is congruent with ADE (Side-Angle-Side congruency).
By CPCTC, angles BEA and DEA are congruent,
which makes them right angles, because they add to straight angle BED.