quadrilaterals, bisectors are parallel

Question

prove that in a quadrilateral ABCD with angle B=90 and D=90 the bisectors of A and C are parallel. ABCD is not a rectangle

Answer 1

The sum $A+C=180°$ so the sum of half of them is $90°$

This means that acute angle $E$ is half $A$ so bisectors are parallel because correspondent angles are congruent

Answer 2

This follows from sum of angles. You have that the sum of the angles $A$ and $C$ is $180$ so the sum of the angles of the bisectors is $90$. Together with the angle sum of a triangle the bisector of $C$ intersect the line through $A$ and $D$ with the same angle as the bisector at $A$.