1, bd bisects angle b, so angle ABE= angle EBC, EF is parallel to BC, so angle FEB= angle EBC= angle ABE, so BF=FE, because AE is perpendicular to BD, so angle EAB=+ angle FBE= 90°, and because angle FBE = angle FEB, angle FEB+ angle AEF = 90°.

2, AB=AD, Angle B= Angle D, AC=AC, so the triangle ADC and triangle ABC are congruent, so Angle DCA= Angle BCA, so AC is equally divided.